Existence of solutions for critical Choquard equations via the concentration compactness method

In this paper we consider the nonlinear Choquard equation $$ -\Delta u+V(x)u =\left(\int_{\mathbb{R}^N}\frac{G(y,u)}{|x-y|^{\mu}}dy\right)g(x,u)\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^N, $$ where \(0

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Bibliographic Details
Published in:arXiv.org 2017-12
Main Authors: Gao, Fashun, da Silva, Edcarlos D, Yang, Minbo, Zhou, Jiazheng
Format: Article
Language:English
Subjects:
Mountains
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Summary:In this paper we consider the nonlinear Choquard equation $$ -\Delta u+V(x)u =\left(\int_{\mathbb{R}^N}\frac{G(y,u)}{|x-y|^{\mu}}dy\right)g(x,u)\hspace{4.14mm}\mbox{in}\hspace{1.14mm} \mathbb{R}^N, $$ where \(0
ISSN:2331-8422