Claudianor O. Alves, Marcos L. Carvalho, “A Lions type result for a large class of Orlicz–Sobolev space and applications”, Mosc. Math. J., 2022, Volume 22, Number 3,Pages <nobr>401

A Lions type result for a large class of Orlicz–Sobolev space and applications

Claudianor O. Alves^a, Marcos L. Carvalho^b

^a Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, 58429-970, Campina Grande - PB, Brazil
^b Instituto de Matemática e Estatística, Universidade Federal de Goias, 74001-970, Goiânia, GO, Brazil

Abstract: 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.

Key words and phrases: Orlicz–Sobolev spaces, variational methods, quasilinear elliptic problems, $\Delta_{2}$-condition, modular.

MSC: 35A15, 35J62, 46E30

Language: English