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Existence and Concentration of Solutions For Sublinear Schrödinger-Poisson Equations

Author

Listed:
  • Anmin Mao

    (Qufu Normal University)

  • Yusong Chen

    (Qufu Normal University)

Abstract

We concern the sublinear Schrödinger-Poisson equations $$\left\{ \begin{gathered} - \Delta u + \lambda V\left( x \right)u + \phi u = f\left( {x,u} \right)in{\mathbb{R}^3} \hfill \\ - \Delta \phi = {u^2}in{\mathbb{R}^3} \hfill \\ \end{gathered} \right.$$ { − 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(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.

Suggested Citation

  • Anmin Mao & Yusong Chen, 2018. "Existence and Concentration of Solutions For Sublinear Schrödinger-Poisson Equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 49(2), pages 339-348, June.
    • Handle: RePEc:spr:indpam:v:49:y:2018:i:2:d:10.1007_s13226-018-0272-9
    DOI: 10.1007/s13226-018-0272-9
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    References listed on IDEAS

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    1. Chun Li & Zeng-Qi Ou & Chun-Lei Tang, 2013. "Existence and Multiplicity of Nontrivial Solutions for a Class of Fourth-Order Elliptic Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, December.
    2. Chunhan Liu & Jianguo Wang, 2013. "Existence of Multiple Solutions for a Class of Biharmonic Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-5, December.
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