ABSTRACT
The chapter closes with applications of the theory to Mechanics. The aim of the chapter is to study the main properties of locally Lipschitz functions whose generalized gradients are pseudo- or quasi-pseudo-monotone. This part is devoted first to the study of the quasi-pseudo-monotone and pseudo-monotone properties of the generalized gradient of nonconvex functions which are the pointwise maxima or minima of finite collections of functions from the QPM and PM classes. When studying variational problems involving nonconvex, nondifferentiable functions one arrives at hemivariational inequalities which are the generalization of the well known in the literature, variational inequalities. As, for variational inequalities the theory of maximal monotone mappings has proved to be the main mathematical tool for establishing existence results, the theory of pseudo-monotone and generalized pseudo-monotone mappings seems to be the main mathematical tool in the theory of hemivariational inequalities.
