Asymptotic Behaviors Of Positive Solutions Of A Class Of Third-order Quasi-linear Differential Equations

In this paper we discuss the asymptotic behaviors of positive solutions of a class of third-order quasi-linear differential equations.First,by discriminating the symbol of the first order derivative,second derivative functions and the third derivative functions of this eventually positive solutions of this kind of equations,we judge the structural of the set of non-oscillation solutions of the equation.Then,by constructing the mapping,using Schauder-Tychonoff fixed point theorem,sufficient conditions for the existence of the non-oscillatory solution which is between the “minimal” solution and “maximal” solution is given.Using the application of the integral inequality,necessary conditions for the existence of the non-oscillatory solution is given.