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2019 Infinitely many solutions for a class of critical Choquard equation with zero mass
Fashun Gao, Minbo Yang, Carlos Alberto Santos, Jiazheng Zhou
Topol. Methods Nonlinear Anal. 54(1): 219-232 (2019). DOI: 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.

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Fashun Gao. Minbo Yang. Carlos Alberto Santos. Jiazheng Zhou. "Infinitely many solutions for a class of critical Choquard equation with zero mass." Topol. Methods Nonlinear Anal. 54 (1) 219 - 232, 2019. https://doi.org/10.12775/TMNA.2019.038

Information

Published: 2019
First available in Project Euclid: 16 July 2019

zbMATH: 07131281
MathSciNet: MR4018277
Digital Object Identifier: 10.12775/TMNA.2019.038

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.54 • No. 1 • 2019
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