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