Multiple solutions for a class of quasilinear problems in Orlicz–Sobolev spaces

Article type: Research Article

Authors: Ait-Mahiout, Karima^{a; *} | Alves, Claudianor O.^b

Affiliations: [a] Laboratoire “Théorie du point fixe et Applications”, École Normale Supérieure, BP 92, Kouba, 16006, Algiers, Algeria. E-mail: karima_ait@hotmail.fr | [b] Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática, CEP:58429-900, Campina Grande – PB, Brazil. E-mail: coalves@mat.ufcg.edu.br

Correspondence: [*] Corresponding author. E-mail: karima_ait@hotmail.fr.

Abstract: This work is concerned with the existence and multiplicity of solutions for the following class of quasilinear problems −ΔΦu+ϕ(|u|)u=h(εx)f(u)in RN,u∈W1,Φ(RN), where Φ(t)=∫0|t|ϕ(s)sds is an N-function, ΔΦ is the Φ-Laplacian operator, ε>0 and h,f are continuous functions. In the proof of our main result we have used Variational methods, Ekeland’s variational principle and some properties of the Nehari manifolds.

Keywords: Variational methods, quasilinear problems, Orlicz–Sobolev space

DOI: 10.3233/ASY-171428

Journal: Asymptotic Analysis, vol. 104, no. 1-2, pp. 49-66, 2017