On existence and concentration behavior of positive ground state solutions for a class of fractional Schrödinger–Choquard equations

Abstract

In this paper, we first employ variational methods to show the existence of positive ground state solutions for fractional Schrodinger–Choquard equations $$\begin{aligned} \varepsilon ^{2s}(-\Delta )^{s}u+Vu=(I_{\alpha }*|u|^p)|u|^{p-2}u,~~~\mathrm {in}~~~\mathbb {R}^{N}, \end{aligned}$$ where potential $$V(x)\in C(\mathbb {R}^{N})$$ is nonnegative and bounded away from 0 as $$|x|\rightarrow \infty $$ , $$I_{\alpha }$$ is the Riesz potential of order $$\alpha \in (0,N)$$ and $$\varepsilon >0$$ is a parameter small enough. When $$V(x)\in C(\mathbb {R}^{N})$$ achieves 0 with a homogeneous behavior, we then investigate the concentration behavior of positive ground state solutions as $$\varepsilon \rightarrow 0^{+}$$ .