On The Eigenvalues Problem for Hemivariational Inequalities: Existence and Stability

This problem can be considered as a nonconvex generalization of the classical variational inequalities of J. L. Lions and G. Stampacchia. For typical examples in connection with mechanics and engineering we refer to the books of Panagiotopoulos [20, 22] and [18]. The techniques used for resolution of hemivariational inequalities are subsequently based on arranging fixed point theorems, Galerkin methods and the convolution product regularization, see [15]-[17], [21], [22] and the bibliography therein. In the last few years, much attention has been focused to the existence theory of such inequalities by means of the generalized Ky Fan minimax theorem [5, 4]. It is the aim of the present paper to investigate the variational-hemivariational inequality (V HI): find u ∈ D and λ ∈ IR such that ∀v ∈ D λ〈H(u), v − u〉 ≤ α (u, v − u) + 〈C (u) , v − u〉