A Perturbation Result for a Double Eigenvalue Hemivariational Inequality with Constraints and Applications

In this paper we prove a perturbation result for a new type of eigenvalue problem introduced by D. Motreanu and P.D. Panagiotopoulos (1998). The perturbation is made in the nonsmooth and nonconvex term of a double eigenvalue problem on a spherlike type manifold considered in Multiple solutions for a double eigenvalue hemivariational inequality on a spherelike type manifold (to appear in Nonlinear Analysis). For our aim we use some techniques related to the Lusternik-Schnirelman theory (including Krasnoselski's genus) and results proved by J.N. Corvellec et al. (1993), M. Degiovanni and S. Lancelotti (1995), and V.D. Rdulescu and P.D. Panagiotopoulos (1998). We apply these results in the study of some problems arising in Nonsmooth Mechanics.