Strong Generalized Nonlinear Random Quasi-Complementarity Problems And A Class Of Random Bilinear Variational Inequalities Problems

The fundamental theory of random variational inequalities and random complementarity problems has played an important role in random functional analysis, the research of this theory and its application is not only has an important influence on random functional analysis theory and its applications, but also provide a powerful tool for the research of all kinds of random equations and random control theorys and its applications. In this thesis, we will study this problem in the following three parts.Firstly, we introduce a class of generalized strong nonlinear random quasi-complementarity problem in the setting of Hilbert space, and study the existence and random interative approach problems of random solutions for this class of random quasi-complementarity problem.Secondly, we introduce and study the existence and uniqueness problems of random solutions for a class of random bilinear variational inequalities by using of auxiliary principle.Finally, Some existence theorems of nonzero solutions and multiple solutions for a class of random bilinear variatinal inequalities are studied in reflexive Banach spaces by random fixed point index approach.