Abstract
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].
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