Eigenvalues of p(x)-Laplacian Dirichlet problem

This paper studies the eigenvalues of the p(x)-Laplacian Dirichlet problem −div(|∇u|p(x)−2∇u) = λ|u|p(x)−2u 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.  2003 Published by Elsevier Inc