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

Fashun Gao, Minbo Yang, Carlos Alberto Santos, Jiazheng Zhou

DOI: http://dx.doi.org/10.12775/TMNA.2019.038

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.

Keywords


Critical Choquard equation; Hardy-Littlewood-Sobolev inequality; infinitely many solutions

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