Infinitely many solutions for a class of critical Choquard equation with zero mass

Abstract

In this paper we investigate the following nonlinear Choquard equation $$ -\Delta u =\bigg(\int_{\mathbb{R}^N}\frac{G(y,u)}{|x-y|^{\mu}}\,dy\bigg)g(x,u)\quad \textrm{in}\ \mathbb{R}^N, $$ where $0< \mu< N$, $N\geq3$, $g(x,u)$ is of critical growth in the sense of the Hardy-Littlewood-Sobolev inequality and $G(x,u)=\int^u_0g(x,s)\,ds$. By applying minimax procedure and perturbation technique, we obtain the existence of infinitely many solutions.