The Periodic And Pseudo-periodic Solutions For Higher Order Coupling Differential Equations

This dissertation mainly studies periodic and pseudo-periodic solutions for higher order coupling differential equations.It is well known that higher order coupling differential equations have wide applications in many fields of sciences.In the present thesis,we deal with periodic and pseudo-periodic solutions for higher order coupling differential equations by exponential dichotomy and the fixed point theory.As for higher order coupling differential equations,the main idea is that we transform higher order coupling differential equations into 1 order nonlinear ones by some special ways.Then,the proof of theorem applies published theory of 1 order nonlinear differential equations.The content of this thesis is organized as follows.This dissertation is divided into four chapters.The first chapter briefly introduces higher order coupling differential equations and knowledge preperation,including the history and background of differential equations,the brief introduction for higher order coupling differential equations,the relationship between exponential dichotomy and solutions for high order coupling differential equations,notations,and mainly results.In chapter two,using exponential dichotomy and fixed point theorem,we give a proof of periodic solutions and existence and uniqueness of pseudo-periodic solutions for higher order coupling differential equations.As an application of theorem 2.2.1,we show two examples to verify this theorem in the third chapter.The end of this dissertation gives a summary,outlook for this dissertation,some references,a brief introduction of the author,and thanks.