Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms

This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Yongxiang Li [verfasserIn] Weifeng Ma [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	elliptic equation gradient term classical solution positive solution

Übergeordnetes Werk:	In: Entropy - MDPI AG, 2003, 24(2022), 12, p 1829
Übergeordnetes Werk:	volume:24 ; year:2022 ; number:12, p 1829

Links:	Link aufrufen Link aufrufen Link aufrufen Journal toc

DOI / URN:	10.3390/e24121829

Katalog-ID:	DOAJ083179798

Internformat


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245	1	0	\|a Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
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520			\|a This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<u</mi<<mo<=</mo<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<u</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mo<∇</mo<<mi<u</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< restricted by the boundary condition <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mrow<<mi<u</mi<<mo<\|</mo<</mrow<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</msub<<mo<=</mo<<mn<0</mn<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< is a bounded domain in <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<</semantics<</math<</inline-formula< with sufficiently smooth boundary <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mo<≥</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<:</mo<<mover<<mo<Ω</mo<<mo<¯</mo<</mover<<mo<×</mo<<mi mathvariant="double-struck"<R</mi<<mo<×</mo<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<<mo<→</mo<<mi mathvariant="double-struck"<R</mi<</mrow<</semantics<</math<</inline-formula< is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< when <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<\|</mo<<mo<(</mo<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<<mo<\|</mo<</mrow<</semantics<</math<</inline-formula< is small or large enough.
650		4	\|a elliptic equation
650		4	\|a gradient term
650		4	\|a classical solution
650		4	\|a positive solution
653		0	\|a Science
653		0	\|a Q
653		0	\|a Astrophysics
653		0	\|a Physics
700	0		\|a Weifeng Ma \|e verfasserin \|4 aut
773	0	8	\|i In \|t Entropy \|d MDPI AG, 2003 \|g 24(2022), 12, p 1829 \|w (DE-627)316340359 \|w (DE-600)2014734-X \|x 10994300 \|7 nnns
773	1	8	\|g volume:24 \|g year:2022 \|g number:12, p 1829
856	4	0	\|u https://doi.org/10.3390/e24121829 \|z kostenfrei
856	4	0	\|u https://doaj.org/article/0497c60252094f9bad7c7d91b3ca56e3 \|z kostenfrei
856	4	0	\|u https://www.mdpi.com/1099-4300/24/12/1829 \|z kostenfrei
856	4	2	\|u https://doaj.org/toc/1099-4300 \|y Journal toc \|z kostenfrei
912			\|a GBV_USEFLAG_A
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912			\|a GBV_ILN_24
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
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912			\|a GBV_ILN_70
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912			\|a GBV_ILN_95
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
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912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_230
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_4012
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4367
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951			\|a AR
952			\|d 24 \|j 2022 \|e 12, p 1829

Indexfelder

author_variant	y l yl w m wm
matchkey_str	article:10994300:2022----::xsecocasclouinfrolnaelpieut
hierarchy_sort_str	2022
callnumber-subject-code	QB
publishDate	2022
allfields	10.3390/e24121829 doi (DE-627)DOAJ083179798 (DE-599)DOAJ0497c60252094f9bad7c7d91b3ca56e3 DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Yongxiang Li verfasserin aut Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<u</mi<<mo<=</mo<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<u</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mo<∇</mo<<mi<u</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< restricted by the boundary condition <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mrow<<mi<u</mi<<mo<\|</mo<</mrow<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</msub<<mo<=</mo<<mn<0</mn<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< is a bounded domain in <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<</semantics<</math<</inline-formula< with sufficiently smooth boundary <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mo<≥</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<:</mo<<mover<<mo<Ω</mo<<mo<¯</mo<</mover<<mo<×</mo<<mi mathvariant="double-struck"<R</mi<<mo<×</mo<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<<mo<→</mo<<mi mathvariant="double-struck"<R</mi<</mrow<</semantics<</math<</inline-formula< is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< when <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<\|</mo<<mo<(</mo<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<<mo<\|</mo<</mrow<</semantics<</math<</inline-formula< is small or large enough. elliptic equation gradient term classical solution positive solution Science Q Astrophysics Physics Weifeng Ma verfasserin aut In Entropy MDPI AG, 2003 24(2022), 12, p 1829 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:24 year:2022 number:12, p 1829 https://doi.org/10.3390/e24121829 kostenfrei https://doaj.org/article/0497c60252094f9bad7c7d91b3ca56e3 kostenfrei https://www.mdpi.com/1099-4300/24/12/1829 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2022 12, p 1829
spelling	10.3390/e24121829 doi (DE-627)DOAJ083179798 (DE-599)DOAJ0497c60252094f9bad7c7d91b3ca56e3 DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Yongxiang Li verfasserin aut Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<u</mi<<mo<=</mo<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<u</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mo<∇</mo<<mi<u</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< restricted by the boundary condition <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mrow<<mi<u</mi<<mo<\|</mo<</mrow<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</msub<<mo<=</mo<<mn<0</mn<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< is a bounded domain in <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<</semantics<</math<</inline-formula< with sufficiently smooth boundary <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mo<≥</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<:</mo<<mover<<mo<Ω</mo<<mo<¯</mo<</mover<<mo<×</mo<<mi mathvariant="double-struck"<R</mi<<mo<×</mo<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<<mo<→</mo<<mi mathvariant="double-struck"<R</mi<</mrow<</semantics<</math<</inline-formula< is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< when <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<\|</mo<<mo<(</mo<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<<mo<\|</mo<</mrow<</semantics<</math<</inline-formula< is small or large enough. elliptic equation gradient term classical solution positive solution Science Q Astrophysics Physics Weifeng Ma verfasserin aut In Entropy MDPI AG, 2003 24(2022), 12, p 1829 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:24 year:2022 number:12, p 1829 https://doi.org/10.3390/e24121829 kostenfrei https://doaj.org/article/0497c60252094f9bad7c7d91b3ca56e3 kostenfrei https://www.mdpi.com/1099-4300/24/12/1829 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2022 12, p 1829
allfields_unstemmed	10.3390/e24121829 doi (DE-627)DOAJ083179798 (DE-599)DOAJ0497c60252094f9bad7c7d91b3ca56e3 DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Yongxiang Li verfasserin aut Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<u</mi<<mo<=</mo<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<u</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mo<∇</mo<<mi<u</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< restricted by the boundary condition <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mrow<<mi<u</mi<<mo<\|</mo<</mrow<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</msub<<mo<=</mo<<mn<0</mn<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< is a bounded domain in <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<</semantics<</math<</inline-formula< with sufficiently smooth boundary <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mo<≥</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<:</mo<<mover<<mo<Ω</mo<<mo<¯</mo<</mover<<mo<×</mo<<mi mathvariant="double-struck"<R</mi<<mo<×</mo<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<<mo<→</mo<<mi mathvariant="double-struck"<R</mi<</mrow<</semantics<</math<</inline-formula< is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< when <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<\|</mo<<mo<(</mo<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<<mo<\|</mo<</mrow<</semantics<</math<</inline-formula< is small or large enough. elliptic equation gradient term classical solution positive solution Science Q Astrophysics Physics Weifeng Ma verfasserin aut In Entropy MDPI AG, 2003 24(2022), 12, p 1829 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:24 year:2022 number:12, p 1829 https://doi.org/10.3390/e24121829 kostenfrei https://doaj.org/article/0497c60252094f9bad7c7d91b3ca56e3 kostenfrei https://www.mdpi.com/1099-4300/24/12/1829 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2022 12, p 1829
allfieldsGer	10.3390/e24121829 doi (DE-627)DOAJ083179798 (DE-599)DOAJ0497c60252094f9bad7c7d91b3ca56e3 DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Yongxiang Li verfasserin aut Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<u</mi<<mo<=</mo<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<u</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mo<∇</mo<<mi<u</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< restricted by the boundary condition <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mrow<<mi<u</mi<<mo<\|</mo<</mrow<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</msub<<mo<=</mo<<mn<0</mn<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< is a bounded domain in <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<</semantics<</math<</inline-formula< with sufficiently smooth boundary <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mo<≥</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<:</mo<<mover<<mo<Ω</mo<<mo<¯</mo<</mover<<mo<×</mo<<mi mathvariant="double-struck"<R</mi<<mo<×</mo<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<<mo<→</mo<<mi mathvariant="double-struck"<R</mi<</mrow<</semantics<</math<</inline-formula< is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< when <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<\|</mo<<mo<(</mo<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<<mo<\|</mo<</mrow<</semantics<</math<</inline-formula< is small or large enough. elliptic equation gradient term classical solution positive solution Science Q Astrophysics Physics Weifeng Ma verfasserin aut In Entropy MDPI AG, 2003 24(2022), 12, p 1829 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:24 year:2022 number:12, p 1829 https://doi.org/10.3390/e24121829 kostenfrei https://doaj.org/article/0497c60252094f9bad7c7d91b3ca56e3 kostenfrei https://www.mdpi.com/1099-4300/24/12/1829 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2022 12, p 1829
allfieldsSound	10.3390/e24121829 doi (DE-627)DOAJ083179798 (DE-599)DOAJ0497c60252094f9bad7c7d91b3ca56e3 DE-627 ger DE-627 rakwb eng QB460-466 QC1-999 Yongxiang Li verfasserin aut Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<u</mi<<mo<=</mo<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<u</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mo<∇</mo<<mi<u</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< restricted by the boundary condition <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mrow<<mi<u</mi<<mo<\|</mo<</mrow<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</msub<<mo<=</mo<<mn<0</mn<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< is a bounded domain in <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<</semantics<</math<</inline-formula< with sufficiently smooth boundary <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mo<≥</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<:</mo<<mover<<mo<Ω</mo<<mo<¯</mo<</mover<<mo<×</mo<<mi mathvariant="double-struck"<R</mi<<mo<×</mo<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<<mo<→</mo<<mi mathvariant="double-struck"<R</mi<</mrow<</semantics<</math<</inline-formula< is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< when <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<\|</mo<<mo<(</mo<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<<mo<\|</mo<</mrow<</semantics<</math<</inline-formula< is small or large enough. elliptic equation gradient term classical solution positive solution Science Q Astrophysics Physics Weifeng Ma verfasserin aut In Entropy MDPI AG, 2003 24(2022), 12, p 1829 (DE-627)316340359 (DE-600)2014734-X 10994300 nnns volume:24 year:2022 number:12, p 1829 https://doi.org/10.3390/e24121829 kostenfrei https://doaj.org/article/0497c60252094f9bad7c7d91b3ca56e3 kostenfrei https://www.mdpi.com/1099-4300/24/12/1829 kostenfrei https://doaj.org/toc/1099-4300 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 24 2022 12, p 1829
language	English
source	In Entropy 24(2022), 12, p 1829 volume:24 year:2022 number:12, p 1829
sourceStr	In Entropy 24(2022), 12, p 1829 volume:24 year:2022 number:12, p 1829
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	elliptic equation gradient term classical solution positive solution Science Q Astrophysics Physics
isfreeaccess_bool	true
container_title	Entropy
authorswithroles_txt_mv	Yongxiang Li @@aut@@ Weifeng Ma @@aut@@
publishDateDaySort_date	2022-01-01T00:00:00Z
hierarchy_top_id	316340359
id	DOAJ083179798
language_de	englisch
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callnumber-first	Q - Science
author	Yongxiang Li
spellingShingle	Yongxiang Li misc QB460-466 misc QC1-999 misc elliptic equation misc gradient term misc classical solution misc positive solution misc Science misc Q misc Astrophysics misc Physics Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
authorStr	Yongxiang Li
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format	electronic Article
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callnumber-label	QB460-466
illustrated	Not Illustrated
issn	10994300
topic_title	QB460-466 QC1-999 Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms elliptic equation gradient term classical solution positive solution
topic	misc QB460-466 misc QC1-999 misc elliptic equation misc gradient term misc classical solution misc positive solution misc Science misc Q misc Astrophysics misc Physics
topic_unstemmed	misc QB460-466 misc QC1-999 misc elliptic equation misc gradient term misc classical solution misc positive solution misc Science misc Q misc Astrophysics misc Physics
topic_browse	misc QB460-466 misc QC1-999 misc elliptic equation misc gradient term misc classical solution misc positive solution misc Science misc Q misc Astrophysics misc Physics
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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hierarchy_parent_title	Entropy
hierarchy_parent_id	316340359
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title	Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
ctrlnum	(DE-627)DOAJ083179798 (DE-599)DOAJ0497c60252094f9bad7c7d91b3ca56e3
title_full	Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
author_sort	Yongxiang Li
journal	Entropy
journalStr	Entropy
callnumber-first-code	Q
lang_code	eng
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publishDateSort	2022
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author_browse	Yongxiang Li Weifeng Ma
container_volume	24
class	QB460-466 QC1-999
format_se	Elektronische Aufsätze
author-letter	Yongxiang Li
doi_str_mv	10.3390/e24121829
author2-role	verfasserin
title_sort	existence of classical solutions for nonlinear elliptic equations with gradient terms
callnumber	QB460-466
title_auth	Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
abstract	This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<u</mi<<mo<=</mo<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<u</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mo<∇</mo<<mi<u</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< restricted by the boundary condition <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mrow<<mi<u</mi<<mo<\|</mo<</mrow<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</msub<<mo<=</mo<<mn<0</mn<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< is a bounded domain in <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<</semantics<</math<</inline-formula< with sufficiently smooth boundary <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mo<≥</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<:</mo<<mover<<mo<Ω</mo<<mo<¯</mo<</mover<<mo<×</mo<<mi mathvariant="double-struck"<R</mi<<mo<×</mo<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<<mo<→</mo<<mi mathvariant="double-struck"<R</mi<</mrow<</semantics<</math<</inline-formula< is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< when <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<\|</mo<<mo<(</mo<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<<mo<\|</mo<</mrow<</semantics<</math<</inline-formula< is small or large enough.
abstractGer	This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<u</mi<<mo<=</mo<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<u</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mo<∇</mo<<mi<u</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< restricted by the boundary condition <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mrow<<mi<u</mi<<mo<\|</mo<</mrow<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</msub<<mo<=</mo<<mn<0</mn<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< is a bounded domain in <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<</semantics<</math<</inline-formula< with sufficiently smooth boundary <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mo<≥</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<:</mo<<mover<<mo<Ω</mo<<mo<¯</mo<</mover<<mo<×</mo<<mi mathvariant="double-struck"<R</mi<<mo<×</mo<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<<mo<→</mo<<mi mathvariant="double-struck"<R</mi<</mrow<</semantics<</math<</inline-formula< is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< when <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<\|</mo<<mo<(</mo<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<<mo<\|</mo<</mrow<</semantics<</math<</inline-formula< is small or large enough.
abstract_unstemmed	This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<−</mo<<mo<Δ</mo<<mi<u</mi<<mo<=</mo<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<u</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mo<∇</mo<<mi<u</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< on <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< restricted by the boundary condition <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<msub<<mrow<<mi<u</mi<<mo<\|</mo<</mrow<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</msub<<mo<=</mo<<mn<0</mn<</mrow<</semantics<</math<</inline-formula<, where <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mo<Ω</mo<</semantics<</math<</inline-formula< is a bounded domain in <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<</semantics<</math<</inline-formula< with sufficiently smooth boundary <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<∂</mo<<mo<Ω</mo<</mrow<</semantics<</math<</inline-formula<, <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<N</mi<<mo<≥</mo<<mn<2</mn<</mrow<</semantics<</math<</inline-formula<, and <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<:</mo<<mover<<mo<Ω</mo<<mo<¯</mo<</mover<<mo<×</mo<<mi mathvariant="double-struck"<R</mi<<mo<×</mo<<msup<<mi mathvariant="double-struck"<R</mi<<mi<N</mi<</msup<<mo<→</mo<<mi mathvariant="double-struck"<R</mi<</mrow<</semantics<</math<</inline-formula< is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mi<f</mi<<mo<(</mo<<mi<x</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<</mrow<</semantics<</math<</inline-formula< when <inline-formula<<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"<<semantics<<mrow<<mo<\|</mo<<mo<(</mo<<mi<ξ</mi<<mo<,</mo<<mspace width="0.166667em"<</mspace<<mi<η</mi<<mo<)</mo<<mo<\|</mo<</mrow<</semantics<</math<</inline-formula< is small or large enough.
collection_details	GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700
container_issue	12, p 1829
title_short	Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
url	https://doi.org/10.3390/e24121829 https://doaj.org/article/0497c60252094f9bad7c7d91b3ca56e3 https://www.mdpi.com/1099-4300/24/12/1829 https://doaj.org/toc/1099-4300
remote_bool	true
author2	Weifeng Ma
author2Str	Weifeng Ma
ppnlink	316340359
callnumber-subject	QB - Astronomy
mediatype_str_mv	c
isOA_txt	true
hochschulschrift_bool	false
doi_str	10.3390/e24121829
callnumber-a	QB460-466
up_date	2024-07-03T16:00:05.811Z
_version_	1803574214198820864
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Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms

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