A class of non-local elliptic system in non-reflexive fractional Orlicz–Sobolev spaces

Abstract

The purpose of this paper is to investigate the existence of a weak solution to a non-local elliptic system, driven by the fractional [Formula: see text]-Laplacian operator in fractional Orlicz–Sobolev space that may be non-reflexive. The non-reflexive case occurs when the Orlicz function [Formula: see text] does not verify the [Formula: see text]-condition.