Arkiv för Matematik

Volume 60 (2022)

Number 1

Multiple solutions for two classes of quasilinear problems defined on a nonreflexive Orlicz–Sobolev space

Pages: 1 – 22



Claudianor O. Alves (Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, Campina Grande, PB, Brazil)

Sabri Bahrouni (Department of Mathematics, Faculty of Sciences, University of Monastir, Tunisia)

Marcos L. M. Carvalho (Instituto de Matemática e Estatística, Universidade Federal de Goias, Goiânia, GO, Brazil)


In this paper we prove the existence and multiplicity of solutions for a large class of quasilinear problems on a nonreflexive Orlicz–Sobolev space. Here, we use the variational methods developed by Szulkin [34] combined with some properties of the weak* topology.


Orlicz–Sobolev spaces, variational methods, quasilinear elliptic problems, $\Delta_2$-condition, modular

2010 Mathematics Subject Classification

35A15, 35J62, 46E30

Received 4 June 2021

Received revised 19 October 2021

Accepted 29 October 2021

Published 16 May 2022