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

[摘要] In this paper we are concerned with some abstract results regarding to fractional Orlicz-Sobolev spaces. Precisely, we ensure the compactness embedding for the weighted fractional Orlicz-Sobolev space into the Orlicz spaces, provided the weight is unbounded. We also obtain a version of Lions' vanishing Lemma for fractional Orlicz-Sobolev spaces, by introducing new techniques to overcome the lack of a suitable interpolation law. Finally, as a product of the abstract results, we use a minimization method over the Nehari manifold to prove the existence of ground state solutions for a class of nonlinear Schrodinger equations, taking into account unbounded or bounded potentials. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-05

[关键词] Fractional Orlicz-Sobolev spaces;Compact embedding;Vanishing and nonvanishing cases;Unbounded or bounded potentials