### Existence of non-trivial solutions for fractional Schrödinger-Poisson systems with subcritical growth

Document Type : Special issue editorial

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

2 Department of Mathematics, Faculty of Basisc Sciences, Babol(Noshirvani) University of Technology Babol, Iran

Abstract

In this paper, we are concerned with the following fractional Schrödinger-Poisson system:
$$\left\{ \begin{array}{ll} (-\Delta^s)u+u+\lambda\phi u=\mu f(n)+|u|^{p-2}|u|, & x\in\mathbb{R}^3 \\ (-\Delta^t)\phi=u^2, & x\in\mathbb{R}^3 \end{array} \right.$$
where $\lambda,\mu$ are two parameters, $s,t \in (0,1], 2t + 4s > 3 ,1 < p ≤ 2_s^∗$ and $f : \mathbb{R} \longrightarrow \mathbb{R}$ is continuous function. Using some critical point theorems and truncation technique, we obtain the existence and multiplicity of non-trivial solutions with the help of the vibrational methods.

Keywords