On a class of generalized Choquard system in fractional Orlicz-Sobolev spaces

Abstract

We study a category of non-homogeneous Choquard systems involving the fractional ϕi(⋅)-Laplacian operator. By establishing suitable hypotheses on the Choquard nonlinearities and the continuous function ϕi, we confirm the existence of nontrivial solutions to the problem at hand. This achievement occurs within the structure of the fractional Orlicz-Sobolev space. Our research makes use of the mountain pass theorem, which circumvents the necessity for the Palais-Smale condition, and strategically leverages the Hardy-Littlewood-Sobolev inequality to enhance our analysis.