On the sub-supersolution method for p(x)-Laplacian equations

This paper deals with the sub-supersolution method for the p(x)-Laplacian equations. A sub-supersolution principle for the Dirichlet problems involving the p(x)-Laplacian is established. It is proved that the local minimizers in the C1 topology are also local minimizers in the W1,p(x) topology for given energy functionals. A strong comparison theorem for the p(x)-Laplacian equations is presented. Some applications of the abstract theorems obtained in this paper to the eigenvalue problems for the p(x)-Laplacian equations are given.