Research On The Stablility And Boundary Value Problem Of Some Kinds Of Differential Equations

The stability and boundary value problems of differential equations are the two main research subjects of differential equations.they are wildly applied in dynamics structural chemistry,the computer information technology,bioengineering,military science,and so on. So a lot of scholars take them seriously,and they have developed fast so far.In this paper, the stability of degenerate differential equations with delay and the BVP of fractional differential equations are mainly discussed.This paper is mainly organized as follows:In the chapter one,we give the history background and significance of the paper and the main jobs of this paper are briefly introduced.In the chapter two we mainly use Razumikhin theorem to discuss the stability of a class of degenerate differential system with variable coefficients and distributed delay,and establish the theorems of the stability of the zero solution for the systems.In the chapter three we mainly study the exponential asymptotic stability for a class of degenerate differential equation with variable delay by using Gronwall-Bellman inequality,at first we give the exponenatial estimation of this differential equation,and then we get several sufficient conditions for the exponenatial asymptotic stability of the zero solution about this differential equation.In the chapter four we use compression mapping principle and Schauder fixed point theorem to discuss a class of fractional differential equation with three point BVP,and then we get the sufficient conditions of the existence and uniqueness for the solution of the BVP.In the chapter five we use the coincidence degree theory due to Mawhin to study the existence of solutions to the BVP of fractional differential equations at resonance on the half line.