A Few Kind Of Hidden Decay Existence And Uniqueness Of Solution Of A

In mathematical physics and many aspects of modern science and technology differential equation has a wide range of applications. Therefore, in recent years, it aroused the attention of many scholars. Concerning the differential equation of theoretical research and practical application there has been many good results.This paper mainly aim at investigate the uniqueness and existence of solutions of a2n-order implicit differential equation and the existence of solutions for the initial condition problems for a Second-order implicit differential equation, the text is divided into five chapters. The first chapter presents the related theory of history and development situation of the initial value problems of differential equation and boundary value problems. And briefly introduce the main job in this paper. The second chapter is some preparation work, mainly introduced the basic definition and lemma of the theory used in this paper. The third chapter we investigate the existence and uniqueness of the solution fourth-order boundary value problems of implicit differential equations by the use of upper and lower solutions method and iterative technique and illustrate the application with practical examples. Finally we give sufficient conditions for the existence and uniqueness of solutions to the boundary value problem of a2n-implicit differential equations. Chapter4study the solvability of boundary value problem of a Second-order implicit differential equations and some existence results are obtained. Chapter5is a summary and prospect of this paper. Chapter3and chapter4are the core parts.