On the Sub-Supersolution Approach for Dirichlet Problems driven by a (p(x), q(x))-Laplacian Operator with Convection Term

The method of sub and super-solution is applied to obtain existence and location of solutions to a quasilinear elliptic problem with variable exponent and Dirichlet boundary conditions involving a nonlinear term f depending on solution and on its gradient. Under a suitable growth condition on the convection term f, the existence of at least one solution satisfying a priori estimate is obtained.