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

2021; Elsevier BV; Volume: 300; Linguagem: Inglês

10.1016/j.jde.2021.08.002

1090-2732

Edcarlos D. Silva, Marcos L. M. Carvalho, José Carlos de Albuquerque, Sabri Bahrouni,

Advanced Mathematical Modeling in Engineering

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 Schrödinger equations, taking into account unbounded or bounded potentials.