Ground state solutions of fractional Choquard equations with general potentials and nonlinearities

Abstract

In the present paper, we consider the following fractional Choquard equation with general potentials and nonlinearities of the form $$\begin{aligned} (-\Delta )^{s}u+V(x)u=\Big (I_{\alpha }*F(u)\Big )f(u),~~~\mathrm {in}~{\mathbb {R}}^{N}, \end{aligned}$$ where $$s\in (0,1)$$ , $$N>2s$$ , $$(-\Delta )^{s}$$ is the fractional Laplacian, $$\alpha \in (0,N)$$ , potential $$V\in C^{1}({\mathbb {R}}^{N},[0,\infty ))$$ , $$I_{\alpha }$$ is a Riesz potential, the nonlinearity F satisfies the general Berestycki–Lions-type assumptions. By introducing some new techniques, we establish the existence of ground state solution of Pohozaev-type to the above equation by variational methods.