Electron. J. Differential Equations, Vol. 2018 (2018), No. 61, pp. 1-15.

Semiclassical ground states for nonlinear Schrodinger-Poisson systems

Hui Zhang, Fubao Zhang

Abstract:
In this article, we study the Schrodinger-Poisson system
$$\displaylines{ -\epsilon^2\Delta u+V(x)u+\phi(x) u=Q(x)u^3,\quad x\in \mathbb{R}^3,\cr -\epsilon^2\Delta\phi=u^2, \quad x\in \mathbb{R}^3, }$$
where $\epsilon>0$ is a parameter, V and Q are positive bounded functions. We establish the existence of ground states for \epsilon small, and describe the concentration phenomena of ground states as $\epsilon\to 0$.

Submitted September 29, 2017. Published March 5, 2018.
Math Subject Classifications: 35J50, 35J60, 35A15.
Key Words: Schrodinger-Poisson system; variational method; concentration; Nehari manifold.

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Hui Zhang
Department of Mathematics
Jinling Institute of Technology
Nanjing 211169, China
email: huihz0517@126.com
  Fubao Zhang
Department of Mathematics
Southeast University
Nanjing 210096, China
email: zhangfubao@seu.edu.cn

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