Perturbations of Eigenvalue Problems with Constraints for Hemivariational Inequalities
The study of hemivariational inequalities began with the pioneering work of Panagiotopoulos (see , , , , , ). This theory extends the framework of variational inequalities to the study of nonconvex energy functionals associated to concrete problems arising in Mechanics, Hysterezis, Phase Transition, Liquid Cristals etc. Panagiotopoulos also defined the notion of nonconvex superpotential, by replacing the subdifferential of a convex function (as in ) with the generalized gradient (in the sense of Clarke) of a locally Lipschitz function. Even if the hemivariational inequalities appear as a generalization of the variational inequalities, they are much more general, in the sense that they are not equivalent to minimum problems but, however, they give rise to substationarity problems. We extend some classical perturbation methods for the framework of hemivariational inequalities and we show how existence results can be obtained for the new problems.
KeywordsVariational Inequality Lipschitz Function Real Hilbert Space Critical Point Theory Distinct Solution
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