Moscow Mathematical Journal

Volume 22, Issue 3, July–September 2022 pp. 401–426.

A Lions Type Result for a Large Class of Orlicz–Sobolev Space and Applications

Authors: Claudianor O. Alves (1) and Marcos L. M. Carvalho (2)
Author institution:(1) Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, 58429-970, Campina Grande - PB, Brazil
(2) Instituto de Matemática e Estatística, Universidade Federal de Goias, 74001-970, Goiânia, GO, Brazil

Summary:

In this paper we prove a Lions type result for a large class of Orlicz–Sobolev space that can be nonreflexive and use this result to show the existence of solution for a large class of quasilinear problem on a nonreflexive Orlicz–Sobolev space.

2020 Math. Subj. Class. 35A15, 35J62, 46E30.

Keywords: Orlicz–Sobolev spaces, variational methods, quasilinear elliptic problems,

$\Delta_{2}$ -condition, modular.

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