EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER-MAXWELL EQUATIONS

In this paper we are concerned with a class of sublinear Schrödinger-Maxwell equations { − Δ u + V ( x ) u + ϕ u = f ( x , u ) , in ℝ 3 , − Δ ϕ = u 2 , lim | x | → + ∞ ϕ ( x ) = 0 , in ℝ 3 , whereV: ℝ3→ ℝ andf: ℝ3× ℝ → ℝ. Under certain assumptions onVandf, some new criteria on the existence and mult...

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Published inTaiwanese journal of mathematics Vol. 17; no. 3; pp. 857 - 872
Main Authors Liu, Zhisu, Guo, Shangjiang, Zhang, Ziheng
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.06.2013
Subjects
Existence theorems
Ground state
Infinity
Mathematical constants
Mathematical functions
Mathematical theorems
Nontrivial solutions
Online AccessGet full text
ISSN1027-5487
2224-6851
DOI10.11650/tjm.17.2013.2202

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Abstract In this paper we are concerned with a class of sublinear Schrödinger-Maxwell equations { − Δ u + V ( x ) u + ϕ u = f ( x , u ) , in ℝ 3 , − Δ ϕ = u 2 , lim | x | → + ∞ ϕ ( x ) = 0 , in ℝ 3 , whereV: ℝ3→ ℝ andf: ℝ3× ℝ → ℝ. Under certain assumptions onVandf, some new criteria on the existence and multiplicity of negative energy solutions for the above system are established via the genus properties in critical point theory. Recent results from the literature are significantly improved. 2010Mathematics Subject Classification: 35J20, 35J65, 35J60. Key words and phrases: Schrödinger-Maxwell equations, Sublinear, Genus, Variational methods.
AbstractList In this paper we are concerned with a class of sublinear Schrödinger-Maxwell equations { − Δ u + V ( x ) u + ϕ u = f ( x , u ) , in ℝ 3 , − Δ ϕ = u 2 , lim | x | → + ∞ ϕ ( x ) = 0 , in ℝ 3 , whereV: ℝ3→ ℝ andf: ℝ3× ℝ → ℝ. Under certain assumptions onVandf, some new criteria on the existence and multiplicity of negative energy solutions for the above system are established via the genus properties in critical point theory. Recent results from the literature are significantly improved. 2010Mathematics Subject Classification: 35J20, 35J65, 35J60. Key words and phrases: Schrödinger-Maxwell equations, Sublinear, Genus, Variational methods.
Author Liu, Zhisu
Guo, Shangjiang
Zhang, Ziheng
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Cites_doi 10.1016/j.jmaa.2010.11.031
10.1142/S021919970800282X
10.1016/S0362-546X(97)00142-9
10.1016/j.jfa.2005.11.010
10.1080/03605309508821149
10.12775/TMNA.1998.019
10.1016/j.jmaa.2008.04.053
10.1017/S030821050000353X
10.4171/RMI/635
10.1007/978-1-4757-2061-7
10.1016/j.na.2011.06.010
10.1515/ans-2002-0205
10.1137/S0036141004442793
10.1016/j.jde.2009.06.017
10.1016/j.na.2009.03.050
10.1016/j.jmaa.2008.03.057
10.1007/s002290170032
10.1142/S0218202505003939
10.1090/cbms/065
10.1016/j.nonrwa.2011.07.027
10.1016/j.na.2010.02.002
10.3934/dcds.2007.18.809
10.1016/j.jmaa.2012.01.057
10.1016/j.na.2011.05.057
10.1016/j.jfa.2006.04.005
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SubjectTerms Existence theorems
Ground state
Infinity
Mathematical constants
Mathematical functions
Mathematical theorems
Nontrivial solutions
Title EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR A CLASS OF SUBLINEAR SCHRÖDINGER-MAXWELL EQUATIONS
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Volume 17
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