Existence et unicité de la solution positive de l'équation TFW sans répulsion électronique
In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.
In this article, we prove the existence of entropy solutions for the Dirichlet problem where is a bounded open set of , , and .
In the present paper, we prove existence results of entropy solutions to a class of nonlinear degenerate parabolic -Laplacian problem with Dirichlet-type boundary conditions and data. The main tool used here is the Rothe method combined with the theory of variable exponent Sobolev spaces.