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

Barnaś S.

Schedae Informaticae

2012

Vol. 21

41--54

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 Chang [4].

Existence result for hemivariational inequality involving p(x)-Laplacian

Barnaś S.

Opuscula Mathematica

2012

Vol. 32, no. 3

439-454

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 Chang [J. Math. Anal. Appl. 80 (1981), 102-129].