Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian

Barnaś, Sylwia

Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 34 (2014) no. 1, pp. 15-39.

Résumé

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.

Détail

Keywords: p(x)-Laplacian, hemivariational inequality, Cerami condition, mountain pass theorem, variable exponent Sobolev space

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