Problems involving the fractional g-Laplacian with lack of compactness

Abstract

In this paper, we prove compact embedding of a subspace of the fractional Orlicz–Sobolev space Ws,GRN consisting of radial functions; our target embedding spaces are of Orlicz type. In addition, we prove a Lions and Lieb type results for Ws,GRN that works together in a particular way to get a sequence whose weak limit is non-trivial. As an application, we study the existence of solutions to quasilinear elliptic problems in the whole space RN involving the fractional g-Laplacian operator, where the conjugated function G̃ of G does not satisfy the Δ2-condition.