Multiplicity of solutions for a class of nonsymmetric eigenvalue hemivariational inequalities

The aim of this paper is to establish the influence of a non-symmetric pert urbation for a symmetric hemivariational eigenvalue inequality with constra ints. The original problem was studied by Motreanu and Panagiotopoulos who deduced the existence of infinitely many solutions for the symmetric case. In this paper it is shown that the number of solutions of the perturbed pro blem becomes larger and larger if the perturbation tends to zero with respe ct to a natural topology. Results of this type in the case of semilinear eq uations have been obtained in [1] Ambrosetti, A. (1974), A perturbation the orem for superlinear boundary value problems, Math. Res. Center, Univ. Wisc onsin-Madison, Tech. Sum. Report 1446; and [2] Bahri, A. and Berestycki, H. (1981), A perturbation method in critical point theory and applications, T rans. Am. Math. Sec. 267, 1-32; for perturbations depending only on the arg ument.