Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains

Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^*-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^*={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\O...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Lancelotti, Sergio [verfasserIn] Molle, Riccardo

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2020

Schlagwörter:	Schrödinger equations Unbounded domains Critical nonlinearity

Anmerkung:	© Springer Nature Switzerland AG 2020

Übergeordnetes Werk:	Enthalten in: Nonlinear differential equations and applications - [Cham (ZG)] : [Springer International Publishing AG], 1994, 27(2020), 1 vom: 04. Jan.
Übergeordnetes Werk:	volume:27 ; year:2020 ; number:1 ; day:04 ; month:01

Links:	Volltext

DOI / URN:	10.1007/s00030-019-0611-5

Katalog-ID:	SPR000318760

Internformat


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520			\|a Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small %${\varepsilon }%$.
650		4	\|a Schrödinger equations \|7 (dpeaa)DE-He213
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700	1		\|a Molle, Riccardo \|4 aut
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912			\|a GBV_ILN_24
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912			\|a GBV_ILN_32
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912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_267
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2056
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4126
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4277
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_4326
912			\|a GBV_ILN_4328
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 27 \|j 2020 \|e 1 \|b 04 \|c 01

Indexfelder

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matchkey_str	article:14209004:2020----::oiieouinfruooosnnnuooosolnaciiaelpip
hierarchy_sort_str	2020
publishDate	2020
allfields	10.1007/s00030-019-0611-5 doi (DE-627)SPR000318760 (SPR)s00030-019-0611-5-e DE-627 ger DE-627 rakwb eng Lancelotti, Sergio verfasserin aut Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2020 Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small %${\varepsilon }%$. Schrödinger equations (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Critical nonlinearity (dpeaa)DE-He213 Molle, Riccardo aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 27(2020), 1 vom: 04. Jan. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:27 year:2020 number:1 day:04 month:01 https://dx.doi.org/10.1007/s00030-019-0611-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2020 1 04 01
spelling	10.1007/s00030-019-0611-5 doi (DE-627)SPR000318760 (SPR)s00030-019-0611-5-e DE-627 ger DE-627 rakwb eng Lancelotti, Sergio verfasserin aut Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2020 Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small %${\varepsilon }%$. Schrödinger equations (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Critical nonlinearity (dpeaa)DE-He213 Molle, Riccardo aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 27(2020), 1 vom: 04. Jan. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:27 year:2020 number:1 day:04 month:01 https://dx.doi.org/10.1007/s00030-019-0611-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2020 1 04 01
allfields_unstemmed	10.1007/s00030-019-0611-5 doi (DE-627)SPR000318760 (SPR)s00030-019-0611-5-e DE-627 ger DE-627 rakwb eng Lancelotti, Sergio verfasserin aut Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2020 Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small %${\varepsilon }%$. Schrödinger equations (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Critical nonlinearity (dpeaa)DE-He213 Molle, Riccardo aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 27(2020), 1 vom: 04. Jan. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:27 year:2020 number:1 day:04 month:01 https://dx.doi.org/10.1007/s00030-019-0611-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2020 1 04 01
allfieldsGer	10.1007/s00030-019-0611-5 doi (DE-627)SPR000318760 (SPR)s00030-019-0611-5-e DE-627 ger DE-627 rakwb eng Lancelotti, Sergio verfasserin aut Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2020 Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small %${\varepsilon }%$. Schrödinger equations (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Critical nonlinearity (dpeaa)DE-He213 Molle, Riccardo aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 27(2020), 1 vom: 04. Jan. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:27 year:2020 number:1 day:04 month:01 https://dx.doi.org/10.1007/s00030-019-0611-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2020 1 04 01
allfieldsSound	10.1007/s00030-019-0611-5 doi (DE-627)SPR000318760 (SPR)s00030-019-0611-5-e DE-627 ger DE-627 rakwb eng Lancelotti, Sergio verfasserin aut Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains 2020 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Nature Switzerland AG 2020 Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small %${\varepsilon }%$. Schrödinger equations (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Critical nonlinearity (dpeaa)DE-He213 Molle, Riccardo aut Enthalten in Nonlinear differential equations and applications [Cham (ZG)] : [Springer International Publishing AG], 1994 27(2020), 1 vom: 04. Jan. (DE-627)271596031 (DE-600)1480580-7 1420-9004 nnns volume:27 year:2020 number:1 day:04 month:01 https://dx.doi.org/10.1007/s00030-019-0611-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_267 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4277 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 27 2020 1 04 01
language	English
source	Enthalten in Nonlinear differential equations and applications 27(2020), 1 vom: 04. Jan. volume:27 year:2020 number:1 day:04 month:01
sourceStr	Enthalten in Nonlinear differential equations and applications 27(2020), 1 vom: 04. Jan. volume:27 year:2020 number:1 day:04 month:01
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Schrödinger equations Unbounded domains Critical nonlinearity
isfreeaccess_bool	false
container_title	Nonlinear differential equations and applications
authorswithroles_txt_mv	Lancelotti, Sergio @@aut@@ Molle, Riccardo @@aut@@
publishDateDaySort_date	2020-01-04T00:00:00Z
hierarchy_top_id	271596031
id	SPR000318760
language_de	englisch
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author	Lancelotti, Sergio
spellingShingle	Lancelotti, Sergio misc Schrödinger equations misc Unbounded domains misc Critical nonlinearity Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains
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topic_title	Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains Schrödinger equations (dpeaa)DE-He213 Unbounded domains (dpeaa)DE-He213 Critical nonlinearity (dpeaa)DE-He213
topic	misc Schrödinger equations misc Unbounded domains misc Critical nonlinearity
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title	Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains
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title_full	Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains
author_sort	Lancelotti, Sergio
journal	Nonlinear differential equations and applications
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author_browse	Lancelotti, Sergio Molle, Riccardo
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doi_str_mv	10.1007/s00030-019-0611-5
title_sort	positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains
title_auth	Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains
abstract	Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small %${\varepsilon }%$. © Springer Nature Switzerland AG 2020
abstractGer	Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small %${\varepsilon }%$. © Springer Nature Switzerland AG 2020
abstract_unstemmed	Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. In such a case, no ground state solution exists and the existence of a bound state solution is proved, for small %${\varepsilon }%$. © Springer Nature Switzerland AG 2020
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title_short	Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains
url	https://dx.doi.org/10.1007/s00030-019-0611-5
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doi_str	10.1007/s00030-019-0611-5
up_date	2024-07-03T15:19:07.247Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR000318760</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230327142754.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2020 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00030-019-0611-5</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR000318760</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00030-019-0611-5-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lancelotti, Sergio</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Nature Switzerland AG 2020</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract The paper concerns with positive solutions of problems of the type %$-\Delta u+a(x)\, u=u^{p-1}+\varepsilon u^{2^-1}%$ in %$\Omega \subseteq \mathbb {R}^N%$, %$N\ge 3%$, %$2^={2N\over N-2}%$, %$2<p<2^*%$. Here %$\Omega %$ can be an exterior domain, i.e. %$\mathbb {R}^N{\setminus }\Omega %$ is bounded, or the whole of %$\mathbb {R}^N%$. The potential %$a\in L^{N/2}_{\mathop {\mathrm{loc}}\nolimits }(\mathbb {R}^N)%$ is assumed to be strictly positive and such that there exists %$\lim _{\|x\|\rightarrow \infty }a(x):=a_\infty >0%$. First, some existence results of ground state solutions are proved. Then the case %$a(x)\ge a_\infty %$ is considered, with %$a(x)\not \equiv a_\infty %$ or %$\Omega \ne \mathbb {R}^N%$. 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Positive solutions for autonomous and non-autonomous nonlinear critical elliptic problems in unbounded domains

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