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

Autor:	Sabri Bahrouni, J.C. de Albuquerque, Marcos L. M. Carvalho, Edcarlos D. Silva
Rok vydání:	2021
Předmět:	Sobolev space Mathematics::Functional Analysis Lemma (mathematics) Pure mathematics Compact space Applied Mathematics Bounded function Embedding Type (model theory) Space (mathematics) Nehari manifold Analysis Mathematics
Zdroj:	Journal of Differential Equations. 300:487-512
ISSN:	0022-0396
DOI:	10.1016/j.jde.2021.08.002
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::00bcd0a5d271b0fb34fbb3d02b737e8e https://doi.org/10.1016/j.jde.2021.08.002 Zobrazit plný text záznamu Full Text from ScienceDirect