The Existence Problem Of Anti-periodic Solutions For Some Kind Of Differential Equations

In recent years, the problem of anti-periodic solutions of differential equations have developed quickly in physics, engineering, medicine and so on.Anti-periodic problems of differential equations have been studied since 1988, H.Okochi studied the anti-periodic solutions of evolution equations with schauder fix points theory, a group of scholar's researching in-depth was carried out. The method of study the cycle was extended to research anti-periodic solutions, and made a lot of meaningful results.The paper contents three chapters. In the first chapter, we introduce the development of the problems of differential equations. In chapter two, we discuss anti-periodic solutions of nonlinear higher order ordinary differential equation, evolution equations and Duffing equations. In chapter three, we study the anti-periodic solutions of impulse equationswith the Schauder fixed point theorem, we prove the existence of anti-periodic solutions. points operator in the Schauder fix points theory.