Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type

Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a loc...
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Gespeichert in:

Autor*in:	Zhang, Jianjun [verfasserIn] do Ó, João Marcos

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2015

Anmerkung:	© Springer Basel 2015

Übergeordnetes Werk:	Enthalten in: Zeitschrift für angewandte Mathematik und Physik - Cham (ZG) : Springer International Publishing AG, 1950, 66(2015), 6 vom: 05. Sept., Seite 3049-3060
Übergeordnetes Werk:	volume:66 ; year:2015 ; number:6 ; day:05 ; month:09 ; pages:3049-3060

Links:	Volltext

DOI / URN:	10.1007/s00033-015-0565-3

Katalog-ID:	SPR000363421

Internformat


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520			\|a Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered.
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912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
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
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_101
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_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_2070
912			\|a GBV_ILN_2086
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_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
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_4012
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_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
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952			\|d 66 \|j 2015 \|e 6 \|b 05 \|c 09 \|h 3049-3060

Indexfelder

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publishDate	2015
allfields	10.1007/s00033-015-0565-3 doi (DE-627)SPR000363421 (SPR)s00033-015-0565-3-e DE-627 ger DE-627 rakwb eng Zhang, Jianjun verfasserin aut Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered. do Ó, João Marcos aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 66(2015), 6 vom: 05. Sept., Seite 3049-3060 (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:66 year:2015 number:6 day:05 month:09 pages:3049-3060 https://dx.doi.org/10.1007/s00033-015-0565-3 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_101 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_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 66 2015 6 05 09 3049-3060
spelling	10.1007/s00033-015-0565-3 doi (DE-627)SPR000363421 (SPR)s00033-015-0565-3-e DE-627 ger DE-627 rakwb eng Zhang, Jianjun verfasserin aut Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered. do Ó, João Marcos aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 66(2015), 6 vom: 05. Sept., Seite 3049-3060 (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:66 year:2015 number:6 day:05 month:09 pages:3049-3060 https://dx.doi.org/10.1007/s00033-015-0565-3 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_101 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_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 66 2015 6 05 09 3049-3060
allfields_unstemmed	10.1007/s00033-015-0565-3 doi (DE-627)SPR000363421 (SPR)s00033-015-0565-3-e DE-627 ger DE-627 rakwb eng Zhang, Jianjun verfasserin aut Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered. do Ó, João Marcos aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 66(2015), 6 vom: 05. Sept., Seite 3049-3060 (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:66 year:2015 number:6 day:05 month:09 pages:3049-3060 https://dx.doi.org/10.1007/s00033-015-0565-3 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_101 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_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 66 2015 6 05 09 3049-3060
allfieldsGer	10.1007/s00033-015-0565-3 doi (DE-627)SPR000363421 (SPR)s00033-015-0565-3-e DE-627 ger DE-627 rakwb eng Zhang, Jianjun verfasserin aut Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered. do Ó, João Marcos aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 66(2015), 6 vom: 05. Sept., Seite 3049-3060 (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:66 year:2015 number:6 day:05 month:09 pages:3049-3060 https://dx.doi.org/10.1007/s00033-015-0565-3 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_101 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_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 66 2015 6 05 09 3049-3060
allfieldsSound	10.1007/s00033-015-0565-3 doi (DE-627)SPR000363421 (SPR)s00033-015-0565-3-e DE-627 ger DE-627 rakwb eng Zhang, Jianjun verfasserin aut Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type 2015 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Springer Basel 2015 Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered. do Ó, João Marcos aut Enthalten in Zeitschrift für angewandte Mathematik und Physik Cham (ZG) : Springer International Publishing AG, 1950 66(2015), 6 vom: 05. Sept., Seite 3049-3060 (DE-627)265506484 (DE-600)1464001-6 1420-9039 nnns volume:66 year:2015 number:6 day:05 month:09 pages:3049-3060 https://dx.doi.org/10.1007/s00033-015-0565-3 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_101 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_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 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_2116 GBV_ILN_2118 GBV_ILN_2119 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_4012 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_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 66 2015 6 05 09 3049-3060
language	English
source	Enthalten in Zeitschrift für angewandte Mathematik und Physik 66(2015), 6 vom: 05. Sept., Seite 3049-3060 volume:66 year:2015 number:6 day:05 month:09 pages:3049-3060
sourceStr	Enthalten in Zeitschrift für angewandte Mathematik und Physik 66(2015), 6 vom: 05. Sept., Seite 3049-3060 volume:66 year:2015 number:6 day:05 month:09 pages:3049-3060
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container_title	Zeitschrift für angewandte Mathematik und Physik
authorswithroles_txt_mv	Zhang, Jianjun @@aut@@ do Ó, João Marcos @@aut@@
publishDateDaySort_date	2015-09-05T00:00:00Z
hierarchy_top_id	265506484
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author	Zhang, Jianjun
spellingShingle	Zhang, Jianjun Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type
authorStr	Zhang, Jianjun
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topic_title	Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type
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title	Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type
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title_full	Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type
author_sort	Zhang, Jianjun
journal	Zeitschrift für angewandte Mathematik und Physik
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author_browse	Zhang, Jianjun do Ó, João Marcos
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author-letter	Zhang, Jianjun
doi_str_mv	10.1007/s00033-015-0565-3
title_sort	standing waves for nonlinear schrödinger equations involving critical growth of trudinger–moser type
title_auth	Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type
abstract	Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered. © Springer Basel 2015
abstractGer	Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered. © Springer Basel 2015
abstract_unstemmed	Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered. © Springer Basel 2015
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title_short	Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type
url	https://dx.doi.org/10.1007/s00033-015-0565-3
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author2	do Ó, João Marcos
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doi_str	10.1007/s00033-015-0565-3
up_date	2024-07-03T15:34:22.610Z
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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">SPR000363421</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230330070915.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201001s2015 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00033-015-0565-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR000363421</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s00033-015-0565-3-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">Zhang, Jianjun</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2015</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 Basel 2015</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we deal with the following singularly perturbed elliptic problem -ε2Δu+V(x)u=f(u),u∈H1(R2),%$\begin{array}{ll}-\varepsilon^2\Delta u+V(x)u=f(u),\quad u \in H^1(\mathbb{R}^2),\end{array}%$where f(s) has critical growth of Trudinger–Moser type. In this paper, we construct a localized bound-state solution concentrating at an isolated component of the positive local minimum points of V as %${\varepsilon \rightarrow 0}%$ under certain conditions on f(s). Our results complete the analysis made in Byeon et al. (Commun Partial Differ Equ 33: 1113–1136, 2008) for the two-dimensional case, in the sense that, in that paper only the subcritical growth was considered.</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">do Ó, João Marcos</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Zeitschrift für angewandte Mathematik und Physik</subfield><subfield code="d">Cham (ZG) : Springer International Publishing AG, 1950</subfield><subfield code="g">66(2015), 6 vom: 05. Sept., Seite 3049-3060</subfield><subfield code="w">(DE-627)265506484</subfield><subfield code="w">(DE-600)1464001-6</subfield><subfield code="x">1420-9039</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:66</subfield><subfield code="g">year:2015</subfield><subfield code="g">number:6</subfield><subfield code="g">day:05</subfield><subfield code="g">month:09</subfield><subfield code="g">pages:3049-3060</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s00033-015-0565-3</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield 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Standing waves for nonlinear Schrödinger equations involving critical growth of Trudinger–Moser type

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