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Existence of solutions for higher order BVP with parameters via critical point theory

Jurkiewicz M., Przeradzki B.

Demonstratio Mathematica

2015

Vol. 48, nr 1

53--61

This paper is concerned with the existence of at least one solution of the nonlinear 2k-th order BVP. We use the Mountain Pass Lemma to get an existence result for the problem, whose linear part depends on several parameters.

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).

On noncoercive elliptic problems with discontinuities

Halidias N.

Journal of Applied Analysis

2003

Vol. 9, nr 2

211-223

In this paper using the critical point theory of Chang [4] for locally Lipschitz functionals we prove an existence theorem for non-coercive Neumann problems with discontinuous nonlinearities. We use the mountain-pass theorem to obtain a nontrivial solution.

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.