Boundedness Of Solutions Based On Fixed Point Theory Of Differential Systems And Practical Stability

As a branch of stability theory of motions, practical stability is a important theory in differential equations, which is more practical than traditional stability. In this paper, firstly, the author study the boundedness and practical stability of the differential system by the extended inequality of Gronwall-Bellman type and Lerray-Schauder's fixed theorm; Secondly, the author discuss the practical stability of some kinds of functional differential equations by the fixed point theory.This paper contains four chapters.In chapter 1,we mainly introduce the developing history of practical stability of differential equations, some methods for studying practical stability and the appliance for the fixed point theory in stability of differential equations. At the same time, we present the organizing structure and the chief contents of this paper.In chapter 2,we introduce some basic concepts,inequalities and the fixed point theories which is prepared for study the practical stability of differential equations in the future.In chapter 3, by using the extended inequalities of Gronwall-Bellman type and Lerray-Schauder's fixed theorem, we study the boundedness and practical stability of solutions for a kind of differential system, and obtain some new conditions.In chapter 4, we discuss the practical stability of the solutions for some kinds of functional differential equation on the given interval are studied by the fixed point theory. Some new conditions about the practical stability are obtained.