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
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Summary: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.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.17.2013.2202