Infinitely many bound state solutions of Choquard equations with potentials

In this paper, we consider the following Choquard equation -Δu+a(x)u=(Iα∗|u|p)|u|p-2u,x∈RN,u(x)→0,|x|→+∞,(CH)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} - \Delta u+a(x)u=(I_\alpha *|u|^p)|u|^{p-2}u, &{}x\in {\mathbb {R}}^N,\\ u(x)\rightarrow 0,&{}|x|\rightarrow +\infty , \end{array}\right. {\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad (\hbox {CH})} \end{aligned}$$\end{document}where N≥3,Iα\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\ge 3, I_\alpha $$\end{document} is a Riesz potential, N+αN<p<N+αN-2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\frac{N+\alpha }{N}<p<\frac{N+\alpha }{N-2}$$\end{document} and a(x) is a given nonnegative potential function. Under some assumptions of asymptotic properties on a(x) at infinity and according to a concentration compactness argument, we obtain infinitely many solutions of (CH), whose energy can be arbitrarily large.