Affiliations: Universidade Federal do Pará, Faculdade de Matemática, 66075-110, Belém, PA, Brazil. E-mail: [email protected] | Universidade Federal de Campina Grande, Unidade Acadêmica de Matemática e Estatística, 58109-970, Campina Grande, PB, Brazil. E-mail: [email protected]
Abstract: This paper is concerned with the multiplicity of nontrivial solutions in an Orlicz–Sobolev space for a nonlocal problem with critical growth, involving N-functions and theory of locally Lipschitz continuous functionals. More precisely, in this paper, we study a result of multiplicity to the following multivalued elliptic problem: −M(∫ΩΦ(|∇u|) dx)ΔΦu∈∂F(·,u)+αh(u) in Ω, u∈W01LΦ(Ω), where Ω⊂RN is a bounded smooth domain, N≥3, M is a continuous function, Φ is an N-function, h is an odd increasing homeomorphism from R to R, α is positive parameter, ΔΦ is the corresponding Φ-Laplacian and ∂F(·,t) stands for Clarke generalized of a function F linked with critical growth. We use genus theory to obtain the main result.
Keywords: Orlicz–Sobolev space, nonlocal problem, multivalued elliptic problem
