Three solutions for singular p-Laplacian type equations

In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(|x|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origi...
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Autor*in:	Huiwen Yan [verfasserIn] Di Geng [verfasserIn] Zhou Yang [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2008

Schlagwörter:	p-Laplacian operator singularity multiple solutions

Übergeordnetes Werk:	In: Electronic Journal of Differential Equations - Texas State University, 2003, (2008), 61, Seite 12
Übergeordnetes Werk:	year:2008 ; number:61 ; pages:12

Links:	Link aufrufen Link aufrufen Journal toc

Katalog-ID:	DOAJ075704250

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allfields	(DE-627)DOAJ075704250 (DE-599)DOAJ6b8f3047d23f4b9ba0243a8b97a8cca4 DE-627 ger DE-627 rakwb eng QA1-939 Huiwen Yan verfasserin aut Three solutions for singular p-Laplacian type equations 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(\|x\|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property. p-Laplacian operator singularity multiple solutions Mathematics Di Geng verfasserin aut Zhou Yang verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2008), 61, Seite 12 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2008 number:61 pages:12 https://doaj.org/article/6b8f3047d23f4b9ba0243a8b97a8cca4 kostenfrei http://ejde.math.txstate.edu/Volumes/2008/61/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2008 61 12
spelling	(DE-627)DOAJ075704250 (DE-599)DOAJ6b8f3047d23f4b9ba0243a8b97a8cca4 DE-627 ger DE-627 rakwb eng QA1-939 Huiwen Yan verfasserin aut Three solutions for singular p-Laplacian type equations 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(\|x\|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property. p-Laplacian operator singularity multiple solutions Mathematics Di Geng verfasserin aut Zhou Yang verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2008), 61, Seite 12 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2008 number:61 pages:12 https://doaj.org/article/6b8f3047d23f4b9ba0243a8b97a8cca4 kostenfrei http://ejde.math.txstate.edu/Volumes/2008/61/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2008 61 12
allfields_unstemmed	(DE-627)DOAJ075704250 (DE-599)DOAJ6b8f3047d23f4b9ba0243a8b97a8cca4 DE-627 ger DE-627 rakwb eng QA1-939 Huiwen Yan verfasserin aut Three solutions for singular p-Laplacian type equations 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(\|x\|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property. p-Laplacian operator singularity multiple solutions Mathematics Di Geng verfasserin aut Zhou Yang verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2008), 61, Seite 12 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2008 number:61 pages:12 https://doaj.org/article/6b8f3047d23f4b9ba0243a8b97a8cca4 kostenfrei http://ejde.math.txstate.edu/Volumes/2008/61/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2008 61 12
allfieldsGer	(DE-627)DOAJ075704250 (DE-599)DOAJ6b8f3047d23f4b9ba0243a8b97a8cca4 DE-627 ger DE-627 rakwb eng QA1-939 Huiwen Yan verfasserin aut Three solutions for singular p-Laplacian type equations 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(\|x\|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property. p-Laplacian operator singularity multiple solutions Mathematics Di Geng verfasserin aut Zhou Yang verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2008), 61, Seite 12 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2008 number:61 pages:12 https://doaj.org/article/6b8f3047d23f4b9ba0243a8b97a8cca4 kostenfrei http://ejde.math.txstate.edu/Volumes/2008/61/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2008 61 12
allfieldsSound	(DE-627)DOAJ075704250 (DE-599)DOAJ6b8f3047d23f4b9ba0243a8b97a8cca4 DE-627 ger DE-627 rakwb eng QA1-939 Huiwen Yan verfasserin aut Three solutions for singular p-Laplacian type equations 2008 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(\|x\|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property. p-Laplacian operator singularity multiple solutions Mathematics Di Geng verfasserin aut Zhou Yang verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2008), 61, Seite 12 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2008 number:61 pages:12 https://doaj.org/article/6b8f3047d23f4b9ba0243a8b97a8cca4 kostenfrei http://ejde.math.txstate.edu/Volumes/2008/61/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 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_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 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_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2008 61 12
language	English
source	In Electronic Journal of Differential Equations (2008), 61, Seite 12 year:2008 number:61 pages:12
sourceStr	In Electronic Journal of Differential Equations (2008), 61, Seite 12 year:2008 number:61 pages:12
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	p-Laplacian operator singularity multiple solutions Mathematics
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container_title	Electronic Journal of Differential Equations
authorswithroles_txt_mv	Huiwen Yan @@aut@@ Di Geng @@aut@@ Zhou Yang @@aut@@
publishDateDaySort_date	2008-01-01T00:00:00Z
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callnumber-first	Q - Science
author	Huiwen Yan
spellingShingle	Huiwen Yan misc QA1-939 misc p-Laplacian operator misc singularity misc multiple solutions misc Mathematics Three solutions for singular p-Laplacian type equations
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topic_title	QA1-939 Three solutions for singular p-Laplacian type equations p-Laplacian operator singularity multiple solutions
topic	misc QA1-939 misc p-Laplacian operator misc singularity misc multiple solutions misc Mathematics
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title	Three solutions for singular p-Laplacian type equations
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title_full	Three solutions for singular p-Laplacian type equations
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title_sort	three solutions for singular p-laplacian type equations
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title_auth	Three solutions for singular p-Laplacian type equations
abstract	In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(\|x\|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property.
abstractGer	In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(\|x\|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property.
abstract_unstemmed	In this paper, we consider the singular $p$-Laplacian type equation $$displaylines{ -hbox{div}(\|x\|^{-eta} a(x, abla u)) =lambda f(x,u),quad hbox{in }Omega,cr u=0,quad hbox{on }partialOmega, }$$ where $0leqeta<N-p$, $Omega$ is a smooth bounded domain in $mathbb{R}^N$ containing the origin, $f$ satisfies some growth and singularity conditions. Under some mild assumptions on $a$, applying the three critical points theorem developed by Bonanno, we establish the existence of at least three distinct weak solutions to the above problem if $f$ admits some hypotheses on the behavior at $u=0$ or perturbation property.
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title_short	Three solutions for singular p-Laplacian type equations
url	https://doaj.org/article/6b8f3047d23f4b9ba0243a8b97a8cca4 http://ejde.math.txstate.edu/Volumes/2008/61/abstr.html https://doaj.org/toc/1072-6691
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Three solutions for singular p-Laplacian type equations

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