On The Study Of The Comparison Theorem Of Three Order Nonlinear Differential Equation

On the basis of the comparison theorem of two order nonlinear differential equation,this paper attempts to study on the comparison theorem of three order nonlineardifferential equation. It mainly composed of four parts.Chapter one will provide the basic concepts related to the later parts and the results thatis necessary.In chapter two, the comparison theorem of the three orders nonlinear and therelative Linear equation will be established based on several Differential inequality.In chapter three, several Sturm comparison theorems of nonlinear differentialequation and linear differential equation will be proved using the theory of differentialequation.Chapter four will provide Picone equation in a much wider sense, and three ordersnonlinear differential equation is studied. Also the relative Sturm theory will be putforward, enriching the relative theory in the modern document.