Multiplicity of solutions for a fractional Schrödinger-Poisson system without (PS) condition

Abstract

In this paper, we study the following fractional Schrödinger-Poisson system $ \begin{equation*} \begin{cases} (-\Delta)^su+V(x)u+\phi u = f(x, u)& x\in\mathbb{R}^3, \\ (-\Delta)^s\phi = u^2& x\in\mathbb{R}^3. \end{cases} \end{equation*} $ Using the variant fountain theorem introduced by Zou [32], we get the existence of infinitely many large energy solutions without the Ambrosetti-Rabinowitz's 4-superlinearity condition. Recent results from the literature are extended and improved.

Keywords

• fractional schrödinger-poisson equation
• variant fountain theorem
• variational methods