Existence and Concentration of Solutions For Sublinear Schrödinger-Poisson Equations

We concern the sublinear Schrödinger-Poisson equations { − Δ u + λ V ( x ) u + ϕ u = f ( x , u ) i n ℝ 3 − Δ ϕ = u 2 i n ℝ 3 where λ > 0 is a parameter, V ∈ C (R 3 ,[0,+∞)), f ∈ C (R 3 ×R,R) and V -1 (0) has nonempty interior. We establish the existence of solution and explore the concentration o...

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Bibliographic Details
Published inIndian journal of pure and applied mathematics Vol. 49; no. 2; pp. 339 - 348
Main Authors Mao, Anmin, Chen, Yusong
Format Journal Article
LanguageEnglish
Published New Delhi Indian National Science Academy 01.06.2018
Springer Nature B.V
Subjects
Applications of Mathematics
Mathematical analysis
Mathematics
Mathematics and Statistics
Numerical Analysis
Schrödinger-Poisson problem
Sublinear
concentration of solutions
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Summary:We concern the sublinear Schrödinger-Poisson equations { − Δ u + λ V ( x ) u + ϕ u = f ( x , u ) i n ℝ 3 − Δ ϕ = u 2 i n ℝ 3 where λ > 0 is a parameter, V ∈ C (R 3 ,[0,+∞)), f ∈ C (R 3 ×R,R) and V -1 (0) has nonempty interior. We establish the existence of solution and explore the concentration of solutions on the set V -1 (0) as λ → ∞ as well. Our results improve and extend some related works.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-018-0272-9