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Hemivariational inequalities governed by the p-Laplacian - Neumann problem

Naniewicz Z.

Control and Cybernetics

2007

Vol. 36, no 3

727-754

A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition. The existence of solutions for problems with Neumann boundary conditions is established by making use of Chang's version of the critical point theory for nonsmooth locally Lipschitz functionals, combined with the Galerkin method. The approach is based on the recession technique introduced previously by the author.

Hemivariational inequalities governed by the p-Laplacian -Dirichlet problem

Naniewicz Z.

Control and Cybernetics

2004

Vol. 33, no 2

181-210

A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition (Naniewicz, 1994). The existence of solutions for problems with Dirichlet boundary conditions is established by making use of Chang's version of the critical point theory for non-smooth locally Lipschitz functionals (Chang, 1981), combined with the Galerkin method. A class of problems with nonlinear potentials fulfilling the classical growth hypothesis without Ainbrosetti-Rabinowitz type assumption is discussed. The approach is based on the recession technique introduced in Naniewicz (2003).

Pseudomonotone semicoercive variational-hemivariational inequalities with unilateral growth condition

Naniewicz Z.

Control and Cybernetics

2003

Vol. 32, no 2

223-244

A variational-hemivariational inequality on a vector valued function space is studied with the nonlinear part satisfying the unilateral growth condition. The higher order term is assumed to be pseudo-monotone and semicoercive. The compatibility condition expressed in terms of a recession functional has been proposed and the existence result has been formulated in a form involving the notion of discontinuous subgradient.

A topological approach to hemivariational inequalities with unilateral growth condition

Motreanu D., Naniewicz Z.

Journal of Applied Analysis

2001

Vol. 7, nr 1

23-41

The present paper is devoted to the study of the existence solution problem for a hemivariational inequality on vector-valued function space in the case when the nonlinear nonconvex part satisfies the unilateral growth condition. The critical point theory combined with the Galerkin approximation method have been used to establish the result.