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Existence and Concentration of Solutions For Sublinear Schrödinger-Poisson Equations

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Abstract

We concern the sublinear Schrödinger-Poisson equations \(\left\{ \begin{gathered} - \Delta u + \lambda V\left( x \right)u + \phi u = f\left( {x,u} \right)in{\mathbb{R}^3} \hfill \\ - \Delta \phi = {u^2}in{\mathbb{R}^3} \hfill \\ \end{gathered} \right.\) where λ > 0 is a parameter, V ∈ C(R3,[0,+∞)), f ∈ C(R3×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.

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Shandong, 273165, P.R. China

    Anmin Mao & Yusong Chen

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  1. Anmin Mao
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  2. Yusong Chen
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Correspondence to Anmin Mao.

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Supported NSFC (11471187, 11571197) and SNSFC (ZR2014AM034)

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Mao, A., Chen, Y. Existence and Concentration of Solutions For Sublinear Schrödinger-Poisson Equations. Indian J Pure Appl Math 49, 339–348 (2018). https://doi.org/10.1007/s13226-018-0272-9

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  • DOI: https://doi.org/10.1007/s13226-018-0272-9

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