Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential
Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Chen, Xiao-Ping [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Qualitative theory of dynamical systems - Basel : Birkhäuser, 1999, 21(2022), 3 vom: 25. Juni |
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| Übergeordnetes Werk: |
volume:21 ; year:2022 ; number:3 ; day:25 ; month:06 |
| Links: |
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| DOI / URN: |
10.1007/s12346-022-00628-4 |
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| Katalog-ID: |
SPR047412496 |
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| 520 | |a Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it. | ||
| 650 | 4 | |a Schrödinger–Poisson system |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Critical growth |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Sign-changing solutions |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Variational methods |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Tang, Chun-Lei |0 (orcid)0000-0001-6911-3597 |4 aut | |
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10.1007/s12346-022-00628-4 doi (DE-627)SPR047412496 (SPR)s12346-022-00628-4-e DE-627 ger DE-627 rakwb eng Chen, Xiao-Ping verfasserin aut Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it. Schrödinger–Poisson system (dpeaa)DE-He213 Critical growth (dpeaa)DE-He213 Sign-changing solutions (dpeaa)DE-He213 Variational methods (dpeaa)DE-He213 Tang, Chun-Lei (orcid)0000-0001-6911-3597 aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 3 vom: 25. Juni (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:3 day:25 month:06 https://dx.doi.org/10.1007/s12346-022-00628-4 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_65 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_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_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 21 2022 3 25 06 |
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10.1007/s12346-022-00628-4 doi (DE-627)SPR047412496 (SPR)s12346-022-00628-4-e DE-627 ger DE-627 rakwb eng Chen, Xiao-Ping verfasserin aut Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it. Schrödinger–Poisson system (dpeaa)DE-He213 Critical growth (dpeaa)DE-He213 Sign-changing solutions (dpeaa)DE-He213 Variational methods (dpeaa)DE-He213 Tang, Chun-Lei (orcid)0000-0001-6911-3597 aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 3 vom: 25. Juni (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:3 day:25 month:06 https://dx.doi.org/10.1007/s12346-022-00628-4 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_65 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_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_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 21 2022 3 25 06 |
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10.1007/s12346-022-00628-4 doi (DE-627)SPR047412496 (SPR)s12346-022-00628-4-e DE-627 ger DE-627 rakwb eng Chen, Xiao-Ping verfasserin aut Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it. Schrödinger–Poisson system (dpeaa)DE-He213 Critical growth (dpeaa)DE-He213 Sign-changing solutions (dpeaa)DE-He213 Variational methods (dpeaa)DE-He213 Tang, Chun-Lei (orcid)0000-0001-6911-3597 aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 3 vom: 25. Juni (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:3 day:25 month:06 https://dx.doi.org/10.1007/s12346-022-00628-4 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_65 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_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_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 21 2022 3 25 06 |
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10.1007/s12346-022-00628-4 doi (DE-627)SPR047412496 (SPR)s12346-022-00628-4-e DE-627 ger DE-627 rakwb eng Chen, Xiao-Ping verfasserin aut Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it. Schrödinger–Poisson system (dpeaa)DE-He213 Critical growth (dpeaa)DE-He213 Sign-changing solutions (dpeaa)DE-He213 Variational methods (dpeaa)DE-He213 Tang, Chun-Lei (orcid)0000-0001-6911-3597 aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 3 vom: 25. Juni (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:3 day:25 month:06 https://dx.doi.org/10.1007/s12346-022-00628-4 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_65 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_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_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 21 2022 3 25 06 |
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10.1007/s12346-022-00628-4 doi (DE-627)SPR047412496 (SPR)s12346-022-00628-4-e DE-627 ger DE-627 rakwb eng Chen, Xiao-Ping verfasserin aut Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it. Schrödinger–Poisson system (dpeaa)DE-He213 Critical growth (dpeaa)DE-He213 Sign-changing solutions (dpeaa)DE-He213 Variational methods (dpeaa)DE-He213 Tang, Chun-Lei (orcid)0000-0001-6911-3597 aut Enthalten in Qualitative theory of dynamical systems Basel : Birkhäuser, 1999 21(2022), 3 vom: 25. Juni (DE-627)582026512 (DE-600)2457088-6 1662-3592 nnns volume:21 year:2022 number:3 day:25 month:06 https://dx.doi.org/10.1007/s12346-022-00628-4 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_65 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_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_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 21 2022 3 25 06 |
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Enthalten in Qualitative theory of dynamical systems 21(2022), 3 vom: 25. Juni volume:21 year:2022 number:3 day:25 month:06 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR047412496</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230507231400.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220626s2022 xx |||||o 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s12346-022-00628-4</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR047412496</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s12346-022-00628-4-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">Chen, Xiao-Ping</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2022</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">© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Schrödinger–Poisson system</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Critical growth</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sign-changing solutions</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Variational methods</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Tang, Chun-Lei</subfield><subfield code="0">(orcid)0000-0001-6911-3597</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Qualitative theory of dynamical systems</subfield><subfield code="d">Basel : Birkhäuser, 1999</subfield><subfield code="g">21(2022), 3 vom: 25. 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Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential Schrödinger–Poisson system (dpeaa)DE-He213 Critical growth (dpeaa)DE-He213 Sign-changing solutions (dpeaa)DE-He213 Variational methods (dpeaa)DE-He213 |
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positive and sign-changing solutions for critical schrödinger–poisson systems with sign-changing potential |
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Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential |
| abstract |
Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 |
| abstractGer |
Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 |
| abstract_unstemmed |
Abstract In this paper, we investigate the following critical Schrödinger–Poisson system -Δu+V(x)u+K(x)ϕu=f(u)+|u|4u,x∈R3,-Δϕ=K(x)u2,x∈R3,%$\begin{aligned} {\left\{ \begin{array}{ll} -\Delta u+V(x)u+K(x)\phi u = f(u)+|u|^4u,\ \ \ &{}\ x \in \mathbb {R}^{3},\\ -\Delta \phi =K(x)u^2, \ \ \ &{}\ x \in \mathbb {R}^{3},\\ \end{array}\right. } \end{aligned}%$where V(x) is a (possible) sign-changing potential, K(x) is a nonnegative function and the nonlinearity %$f\in \mathcal {C}(\mathbb {R},\mathbb {R})%$. By using variational methods with a more general global compactness lemma, we obtain a positive least energy solution and a least energy sign-changing solution with exactly two nodal domains, and we also prove that the energy of least energy sign-changing solution is strictly larger than twice that of least energy solutions. Moreover, this paper further analyzes the exponential decay of the positive least energy solution given by Liu, Liao and Tang (Nonlinearity30 (2017), 899–911), and can be regarded as the supplementary work of it. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022 |
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Positive and Sign-changing Solutions for Critical Schrödinger–Poisson Systems with Sign-changing Potential |
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https://dx.doi.org/10.1007/s12346-022-00628-4 |
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Tang, Chun-Lei |
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10.1007/s12346-022-00628-4 |
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| score |
7.401634 |