Solutions and multiple solutions for p(x)-Laplacian equations with nonlinear boundary condition

Abstract

The authors study the p(x)-Laplacian equations with nonlinear boundary condition. By using the variational method, under appropriate assumptions on the perturbation terms f1(x, u), f2(x, u) and h1(x), h2(x), such that the associated functional satisfies the “mountain pass lemma” and “fountain theorem” respectively, the existence and multiplicity of solutions are obtained. The discussion is based on the theory of variable exponent Lebesgue and Sobolev spaces.