Fractional Schrödinger–Poisson system involving concave and convex nonlinearities

Abstract

In this paper, we investigate the following fractional Schrödinger–Poisson system:

where $1<p<2<q<+\infty$, $(-\Delta {)}^s$ denotes the fractional Laplacian of order $s\in (\frac{3}{4},1)$, and $V(x)$, $P(x)$, and $Q(x)$ are given functions satisfying certain conditions. We aim to establish the existence of infinitely many solutions for this system, considering nonlinearities $P(x)|u{|}^{p-2}u$ and $Q(x)|u{|}^{q-2}u$ with varying growth rates, including subcritical, critical, and supercritical cases.