Compact embedding theorems and a Lions' type Lemma for fractional Orlicz–Sobolev spaces

In this paper we are concerned with some abstract results regarding to fractional Orlicz-Sobolev spaces. Precisely, ensure the compactness embedding for weighted space into Orlicz spaces, provided weight is unbounded. We also obtain a version of Lions' “vanishing” Lemma by introducing new techniques overcome lack suitable interpolation law. Finally, as product results, use minimization method over Nehari manifold prove existence ground state solutions class nonlinear Schrödinger equations, taking account unbounded or bounded potentials.