Electron. J. Differential Equations, Vol. 2017 (2017), No. 97, pp. 1-13.

Infinitely many solutions for fractional Schrodinger-Poisson systems with sign-changing potential

Jianhua Chen, Xianhua Tang, Huxiao Luo

Abstract:
In this article, we prove the existence of multiple solutions for following fractional Schrodinger-Poisson system with sign-changing potential
$$\displaylines{ (-\Delta)^s u+V(x)u+\lambda\phi u=f(x,u),\quad x\in\mathbb{R}^3,\cr (-\Delta)^t\phi=u^2,\quad x\in\mathbb{R}^3, }$$
where $(-\Delta)^\alpha$ denotes the fractional Laplacian of order $\alpha\in(0,1)$, and the potential V is allowed to be sign-changing. Under certain assumptions on f, we obtain infinitely many solutions for this system.

Submitted June 28, 2016. Published April 5, 2017.
Math Subject Classifications: 35J60, 35J20.
Key Words: Fractional Schrodinger-Poisson systems; sign-changing potential; symmetric mountain pass theorem; infinitely many solutions.

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Jianhua Chen
School of Mathematics and Statistics
Central South University
Changsha, Hunan 410083, China
email: cjh19881129@163.com
Xianhua Tang
School of Mathematics and Statistics
Central South University
Changsha, Hunan 410083, China
email: tangxh@mail.csu.edu.cn
Huxiao Luo
School of Mathematics and Statistics
Central South University
Changsha, Hunan 410083, China
email: wshrm7@126.com

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