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Existence Result for Differential Inclusion with p(x)-Laplacian

100%

Barnaś S.

Schedae Informaticae

2012

tom 21

In this paper we study the nonlinear elliptic problem with p(x)-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to ChangIn this paper we study the nonlinear elliptic problem with p(x)-Laplacian (hemivariational inequality). We prove the existence of a nontrivial solution. Our approach is based on critical point theory for locally Lipschitz functionals due to Chang

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

100%

Barnaś S.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2014

tom 34

nr 1

15-39

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.