Eigenvalue Problems For Hemivariational Inequalities Research Articles

A hemivariational inequality involving [formula omitted]-Laplacian on an infinite strip

This paper deals with an eigenvalue problem for hemivariational inequalities on domains of the type ω × R ( ω is a bounded open subset of R N − 1 , N ≥ 2 ) and it involves concave–convex nonlinearities. Under suitable conditions on the nonlinearities, two nontrivial solutions are obtained which belong to a special closed convex cone of W 0 1 , p ( ω × R ) whenever the eigenvalues are of certain range. Our approach is variational based on the theories of non-smooth analysis. Our results are a generalization of the case of Laplacian from A. Kristály, et al. to the case of p -Laplacian.

Positive solutions and multiple solutions at non-resonance, resonance and near resonance for hemivariational inequalities with 𝑝-Laplacian

In this paper we study eigenvalue problems for hemivariational inequalities driven by thepp-Laplacian differential operator. We prove the existence of positive smooth solutions for both non-resonant and resonant problems at the principal eigenvalue of the negativepp-Laplacian with homogeneous Dirichlet boundary condition. We also examine problems which are near resonance both from the left and from the right of the principal eigenvalue. For nearly resonant from the right problems we also prove a multiplicity result.

An eigenvalue problem for hemivariational inequalities with combined nonlinearities on an infinite strip

In this paper a class of eigenvalue problems for hemivariational inequalities is studied which is defined on domains of the type ω × R ( ω is a bounded open subset of R m , m ⩾ 1 ) and it involves concave–convex nonlinearities. Under suitable conditions on the nonlinearities, two nontrivial solutions are obtained which belong to a special closed convex cone of H 0 1 ( ω × R ) whenever the eigenvalues are of certain range. Our approach is variational, the main tool in our investigation is the critical point theory developed by Motreanu and Panagiotopoulos [Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities, Kluwer Academic Publishers, Dordrecht, 1999, Chapter 3].

Multiplicity Results for an Eigenvalue Problem for Hemivariational Inequalities in Strip-Like Domains

In this paper we study the multiplicity of solutions for a class of eigenvalue problems for hemivariational inequalities in strip-like domains. The first result is based on a recent abstract theorem of Marano and Motreanu, obtaining at least three distinct, axially symmetric solutions for certain eigenvalues. In the second result, a version of the fountain theorem of Bartsch which involves the nonsmooth Cerami compactness condition, provides not only infinitely many axially symmetric solutions but also axially nonsymmetric solutions in certain dimensions. In both cases the principle of symmetric criticality for locally Lipschitz functions plays a crucial role.

Perturbations of Hemivariational Inequalities with Constraints andApplications

The aim of the present paper is to discuss the influence which certain perturbations have on the solution of the eigenvalue problem for hemivariational inequalities on a sphere of given radius. The perturbation results in adding a term of the type g^0(x, u(x); v(x)) to the hemivariational inequality, where g is a locally Lipschitz nonsmooth and nonconvex energy functional. Applications illustrate the theory.

A Bifurcation Theory for a Nonconvex Unilateral Laminated Plate Problem Formulated as a Hemivariational Inequality Involving a Potential Operator

AbstractThe present paper concerns the hemivariational inequality approach to the laminated plate theory under abstract subdifferential conditions. The mechanical problem is formulated as a nonlinear eigenvalue problem for hemivariational inequalities and a corresponding bifurcation theory is given.

On the Eigenvalue Problem for Hemivariational Inequalities: Existence and Multiplicity of Solutions

In this article the eigenvalue problem for hemivariational inequalities is studied. First some existence results are obtained by applying a critical point method suitable for nonconvex nonsmooth energy functions. Further some results concerning the multiplicity of solutions are proved. Applications from mechanics illustrate the theory.

A minimax approach to the eigenvalue problem of hemivariational inequalities and applications

The aim of the present paper is the study of the eigenvalue problem for hemivariational inequalities. The minimax approach applied (Mountain-Pass Theorem) is a generalization, proved in this paper, of a result of Rabinowitz for nonsmooth functionals. The main result of the paper states the existence of a nontrivial solution for the eigenvalue problem. Applications concerning yet unsolved mechanical problems illustrate the theory.