Multiple solutions for a nonhomogeneous Dirichlet problem in Orlicz–Sobolev spaces

摘要

In this paper, moving within the framework of Orlicz–Sobolev spaces, we guarantee through variational arguments the existence of three weak solutions to the nonhomogeneous boundary value problem: -div(a(|∇u(x)|)∇u(x))=λf(x,u)+μg(x,u)inΩ,u=0on∂Ω, with Ω bounded domain in Rn with smooth boundary ∂Ω,λ,μ real parameters, f,g:Ω×R→R Carathéodory functions and the function t→a(|t|)t odd, increasing homeomorphism from R onto R. Applications and comparisons are also presented; in particular, we improve a result for an eigenvalue problem established by Mihăilescu and Repovš in [15].