Abstract
Under suitable assumptions, we study the existence of a weak nontrivial solution for the following Steklov problem involving the p(x)-Laplacian
{Delta(p(x))u = a(x)|u|(p(x)-2)u in Omega,
|del u|(p(x)-2) partial derivative u/partial derivative v = lambda V (x)|u|(q(x)-2)u on partial derivative Omega.
Our approach is based on min-max method and Ekeland's variational principle.