Research On Existence And Uniqueness Of Anti-periodic Solutions For Several Kinds Of Differential Equations

This thesis mainly deals with the existence and uniqueness of anti-periodic solutions for several kinds of differential system. This paper is composed of four chapters. The organization of this thesis is as follows.In Chapter1, we simply introduce the development and basic information of anti-periodic solutions.In Chapter2. we study an semilinear fractional differential equations. Some sufficient conditions on the existence of anti-periodic mild solution for the the system is obtained by Banach contraction mapping principle.In Chapter3, we study an semilinear evolution equation. By applying semigroup theory. Banach contraction mapping principle and Schauder’s fixed point theorem, some new criteria are established for the existence of anti-periodic mild solutions for this system and extend some related result.In Chapter4. by using Leray-Schauder degree theory, we establish some new results on the existence and uniqueness of anti-periodic solution for a kind of nth-order differential equations with continuously distributed delays. We give an example to demonstrate the applications of our results.