Bound states of fractional Choquard equations with Hardy-Littlewood-Sobolev critical exponent

We deal with the following fractional Choquard equation [GRAPHICS] . where I-mu(x) is the Riesz potential, s is an element of (0, 1), 2s< N not equal 4s, 0 < mu < min{N, 4s} and 2* mu,s= 2N- mu/N-2s is the fractional critical Hardy-Littlewood-Sobolev exponent. By combining variational methods and the Brouwer degree theory, we investigate the existence and multiplicity of positive bound solutions to this equation when V(x) is a positive potential bounded from below. The results obtained in this paper extend and improve some recent works in the case where the coefficient V(x) vanishes at infinity. (c) 2023 Elsevier Inc. All rights reserved.

Automated summary

In this paper, we investigate the existence and multiplicity of positive bound solutions to the fractional Choquard equation with a positive potential bounded from below. By combining variational methods and the Brouwer degree theory, we obtain extended and improved results in the case where the coefficient V(x) vanishes at infinity.