Existence of Ground State Solutions for Choquard Equation with the Upper Critical Exponent

Author:

Abdullah Qadha Sarah12,Chen Haibo1,Qadha Muneera Abdullah12

Affiliation:

1. School of Mathematics and Statistics, Central South University, Changsha 410083, China

2. Department of Mathematics, Faculty of Education at Al-Mahweet, Sana’a University, Al-Mahweet 1247, Yemen

Abstract

In this article, we investigate the existence of a nontrivial solution for the nonlinear Choquard equation with upper critical exponent see Equation (6). The Riesz potential in this case has never been studied. We establish the existence of the ground state solution within bounded domains Ω⊂RN. Variational methods are used for this purpose. This method proved to be instrumental in our research, enabling us to address the problem effectively. The study of the existence of ground state solutions for the Choquard equation with a critical exponent has applications and relevance in various fields, primarily in theoretical physics and mathematical analysis.

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

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