Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator

摘要

We prove the existence of weak solutions to the Dirichlet boundary valueproblem for equations involving the p(x)-Laplacian-like operator in the principal part,with reaction term satisfying a sub-critical growth condition. We establish the existenceof at least one nontrivial weak solution and three weak solutions, by using variationalmethods and critical point theory.