Existence Of Solutions For A Quasi Variational Inequality

Quasi-variational inequality with applications in economic equilibrium,biological sci-ences,engineering,etc.Generalized Nash equilibrium problem under certain conditions can be transformed into quasi-variational inequality problems,Existence of solutions for quasi-variational inequality problem is a basic problem and has been studied by several classical methods:fixed-point theory,KKM-theorem.This article mainly use fixed point index and exceptional family of elements to study the existence of quasi-variational inequality problems solutions and boundedness.It is organized as follows:In Chapter 1,we introduce the background of quasi-variational inequality,the develop-ment of degree theory and exceptional family,and list some basic conceptions and lemmas which are used is this dissertation.In Chapter 2,we define a class of generalized projection operator and properties of gen-eralized projection operator and the theorems of quasi-variational inequality is transformed into Leary-Schauder type fixed point theorem.In Chapter 3,a fixed point index theory of set-valued mapping is established,and the fixed point index is employed to prove some coercivity conditions to the existence theorems of solutions for quasi-variational inequality problems.In Chapter 4,firstly we give a Leary-Schauder type fixed point theorem for set-valued mapping in reflexive Banach spaces.Then,a new concept of exceptional family for quasi-variational inequality,the equivalence between the nonexistence of solution for quasi-variational inequality problems and the the existence exception family of elements is established.In ad-dition some coercivity conditions for existence theorems of solutions for quasi-variational inequality problems is presented.