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

Silva, Edcarlos D. ; Carvalho, M.L. ; de Albuquerque, J.C. ; Bahrouni, Sabri

Journal of Differential Equations, 2021-11, Vol.300, p.487-512 [Periódico revisado por pares]

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Título:
Compact embedding theorems and a Lions' type Lemma for fractional Orlicz–Sobolev spaces
Autor: Silva, Edcarlos D. ; Carvalho, M.L. ; de Albuquerque, J.C. ; Bahrouni, Sabri
Assuntos: Compact embedding ; Fractional Orlicz-Sobolev spaces ; Unbounded or bounded potentials ; Vanishing and nonvanishing cases
É parte de: Journal of Differential Equations, 2021-11, Vol.300, p.487-512
Descrição: 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.
Editor: Elsevier Inc
Idioma: Inglês

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