| In recent years, research about the stability of the solution set of nonlinear problems is very active, especially about essential point, essential set and essential component. Yu (2004) has derived the unified existence theorem of essential components. In this thesis, another existence theorem of essential components of some set-valued mappings is first given. From this theorem, we derive existence theorems of essential components of solution sets of some nonlinear problems.It consists of three chapters.Chapter one is the preliminaries. We briefly introduce some concepts, properties and important results which will be used in this thesis, including the continuity of set-valued mapping and the concept about stability, etc.In chapter two, an existence theorem of essential components of some set-valued mappings is proved while its generalization is obtained. From this theorem and its generalization, we prove the stability of essential components of the set of fixed points, Ky Fan's points and the solution set of nonlinear complementary problem. We also study the generic stability of the solution set of nonlinear complementary problem.In chapter three, we consider the optimization problems and the system of nonlinear equations. As we show, if the optimum solution set of optimization problem and the global solution set of system of nonlinear equations can be divided into two or more different components, there is no essential component. By using the existence theorem of essential components, we make a few remarks on the two problems. |
