Electron. J. Differential Equations, Vol. 2017 (2017), No. 231, pp. 1-13.

Existence of positive ground state solutions for a class of asymptotically periodic Schrodinger-Poisson systems

Da-Bin Wang, Hua-Fei Xie, Wen Guan

Abstract:
In this article, by using variational method, we study the existence of a positive ground state solution for the Schr\"odinger-Poisson system
$$\displaylines{ -\Delta u+V(x)u+K(x)\phi u=f(x,u),\quad x\in\mathbb{R}^3,\cr -\Delta\phi=K(x)u^2,\quad x\in\mathbb{R}^3, }$$
where V(x), K(x) and f(x,u) are asymptotically periodic functions in x at infinity.

Submitted March 22, 2017. Published September 22, 2017.
Math Subject Classifications: 35J20, 35J60, 35J65.
Key Words: Schrodinger-Poisson systems; ground state solution; variational methods.

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Da-Bin Wang
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu 730050, China
email: wangdb96@163.com
Hua-Fei Xie
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu 730050, China
email: xiehuafeilz@163.com
Wen Guan
Department of Applied Mathematics
Lanzhou University of Technology
Lanzhou, Gansu 730050, China
email: mathguanw@163.com

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