Existence Of Solutions For Two Class Of Hemi-variational Inequalities

Iin first part of this thesis,we discuss the following nonlinear parabolic hemi-variational inequality problem:Find u ∈X,(?)(the dual of X)and(?)Where(?)be a bounded domain with C2-boundary(?)(?)(?)stands for the generalizcd subdifferential of j(x,t,u)at,u.By using the nonsmooth critical point theory,we study the existence of solution of this problem.In second part of this thesis,we study the following nonlinear elliptic hemi-variational inequality on unbounded domains:Find u∈κC such that(?)·Where(?)be a unbounded domain.V denote the usual Sobolev space(?)(?)is the nonlinear multivalued map.j:(?)(?)Due to unbounded,it is unfounded to compact embedding of the Sobolev spaces.By using the Clarke generalized directional derivatives for-locally Lipschitz functions and some nonlinear function analysis techniques,such as the Ky Fan theorem for multivalued mappings,etc,we obtain the existence of solutions of this problem.