Eigenvalues of p(x)-Laplacian Dirichlet problem

Abstract This paper studies the eigenvalues of the p(x)-Laplacian Dirichlet problem − div (|∇u| p(x)−2 ∇u)=λ|u| p(x)−2 u in Ω, u=0 on ∂Ω, where Ω is a bounded domain in RN and p(x) is a continuous function on Ω such that p(x)>1. We show that Λ, the set of eigenvalues, is a nonempty infinite set such that supΛ=+∞. We present some sufficient conditions for infΛ=0 and for infΛ>0, respectively.

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