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. Rădulescu and P.D. Panagiotopoulos (1998). We apply these results in the study of some problems arising in Nonsmooth Mechanics.

[1]  P. Panagiotopoulos,et al.  On the Eigenvalue Problem for Hemivariational Inequalities: Existence and Multiplicity of Solutions , 1996 .

[2]  P. Panagiotopoulos,et al.  A variational-hemivariational inequality approach to the laminated plate theory under subdifferential boundary conditions , 1988 .

[3]  P. Panagiotopoulos.  Inequality Problems in Mechanics and Applications: Convex and Nonconvex Energy Functions , 1985 .

[4]  P. Panagiotopoulos,et al.  An eigenvalue problem for a hemivariational inequality involving a nonlinear compact operator , 1995 .

[5]  Panagiotis D. Panagiotopoulos,et al.  Nonconvex Problems of Semipermeable Media and Related Topics , 1985, 1985.

[6]  Vicentiu D. Radulescu,et al.  Perturbations of Hemivariational Inequalities with Constraints and Applications , 1998, J. Glob. Optim..

[7]  P. Panagiotopoulos.  Nonconvex Superpotentials and Hemivariational Inequalities. Quasidifferentiability in Mechanics , 1988 .

[8]  F. Clarke.  Optimization And Nonsmooth Analysis , 1983 .

[9]  P. Panagiotopoulos,et al.  Multiple solutions for a double eigenvalue hemivariational inequality on a sphere-like type manifold , 2000 .

[10]  Double Eigenvalue Problems for Hemivariational Inequalities , 1997 .

[11]  R. Ho.  Algebraic Topology , 2022 .

[12]  P. D. Panagiotopoulos,et al.  Mathematical Theory of Hemivariational Inequalities and Applications , 1994 .

[13]  P. Panagiotopoulos.  Semicoercive hemivariational inequalities. On the delamination of composite plates , 1989 .

[14]  Dumitru Motreanu,et al.  Nonconvex energy functions, related eigenvalue hemivariational inequalities on the sphere and applications , 1995, J. Glob. Optim..

[15]  Marco Degiovanni,et al.  Deformation properties for continuous functionals and critical point theory , 1993 .

[16]  Global Bifurcation in Variational Inequalities , 1997 .

[17]  R. T. Rockafellar,et al.  La théorie des sous-gradients et ses applications à l'optimisation : fonctions convexes et non convexes , 1979 .

[18]  Marco Degiovanni,et al.  Perturbations of even nonsmooth functionals , 1995, Differential and Integral Equations.

[19]  Kung-Ching Chang,et al.  Variational methods for non-differentiable functionals and their applications to partial differential equations , 1981 .

[20]  P. D. Panagiotopoulos,et al.  Nonconvex energy functions. Hemivariational inequalities and substationarity principles , 1983 .