The Essential Components Of Solutions Of Some Kinds Of Economic Models

In this thesis, we focus on the stability of solutions of some kinds of nonlinear problems. We firstly investigate both the existence of essential components of equilibrium point sets of Warlas economic models and that of equilibrium point sets of production economic models by a unified approach in Yu et al.(2004). Then we give a new condition of the existence of essential components in a unified approach. Applying this new condition, we prove the existence of essential components of the set of fixed points under Hausdorff graph topology, and deduce the existence of essential components of the set of KKM points, the set of solutions of Ky Fan Section Theorem and the set of solutions of Ky Fan Lemma. In addition, we study the generic stability of vector-valued Ky Fan points. This thesis is organized as follows.Chapter 1 We recall some notions and results used in our analysis in this thesis, including some basic concepts about topological space theory, continuity of set-valued mappings and some results about essential sets and essential components.Chapter 2 This chapter is devoted to deducing both the existence of essential components of equilibrium point sets of Walras economics and that of equilibrium point sets of production economics by a unified approach in Yu et al. (2004).Chapter 3 This chapter is devoted to making further discussion to the existence theorem of essential components. Firstly, we get a new condition of the existence essential components in a unified approach. As applications, we prove the existence of essential component of the set of fixed points under graph topology, and also deduce the existence of essential components of the set of KKM points, the set of solutions of Ky Fan Section Theorem and the set of solutions of Ky Fan Lemma.Chapter 4 We study the stability of vector-valued Ky Fan points. We first introduce some basic concepts about vector set-valued mappings. Then we prove the existence of vector-valued Ky Fan points in two cases: the one is in the compact setting and the other is in the non-compact setting. Finally, we study the generic stability of vector-valued Ky Fan points in compact setting.