In this paper, we consider the existence of multiple solutions for the following p(x)-Laplacian equations with critical Sobolev growth conditions
−div(|∇u| p(x)−2 ∇u) + |u| p(x)−2 u = f(x, u) in Ω,
u = 0 on ∂Ω.
We show the existence of infinitely many pairs of solutions by applying the Fountain Theorem and the Dual Fountain Theorem respectively. We also present a variant of the concentration-compactness principle, which is of independent interest.
Available at: http://works.bepress.com/chunshan_zhao/12/