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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).