Sturm Comparison Theory And Zero Theory Of Solution For The Third Order Differential Equations

Abstract:Both the third order linear differential equations theory of Sturm comparison theory and zero points theory are given on the basis of the Sturm com-parison theory and zero theory of solution for the second,which are studied in depth. the main contents of this paper is as follows:1. Some basic concepts and important lemmas about Sturm comparison theory and zero theory of solution for differential equations are intruduced for the use of chapter 2 and 3.2. Discussion of three-order Sturm comparison theorem of differential equa-tions. Given a special three-order Sturm comparison theorem of linear homogeneous differential equations, and on this basis that most Sturm comparison theorem and oscillation comparison theorems.3. Study on the theory of third order differential equation zero points theory. First,the concepts of distance between adjacent zero points are given, some good results are obtained.