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摘要
In this paper, we consider the existence of multiple solutions for the following p(x)-Laplacian equations with critical Sobolev growth conditions
{ -div(vertical bar del u vertical bar(p(x)-2) del u) + vertical bar u vertical bar(p(x)-2) u = f(x, u) in Omega,
u = 0 on partial derivative Omega.
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.
