Qualitative Study On Several Classes Of Differential And Difference Equations

This thesis of Master is composed of four chapters, which mainly studied the existence of non-oscillatory solutions of a class of higher-order nonlinear neutral difference equations with a forced term, oscillation criteria for a class of difference equations ,global attractivity for a class of nonautonomous variable delay-logistic equation,and existence of periodic solutions for differential equation with several delays.In chapter one, by using Krasnoselskii's fixed point theorem, necessary and sufficient conditions of the existence of non-oscillatory solutions of a class of higher-order nonlinear neutral difference equation with a forced term are obtained. Our results extend the results of the some known results.Chapter two , sufficient conditions of oscillation of all solutions for the first order delay difference equation with two delays are obtained , and we use the criteria to the difference equation with several delays. Our results extend the known results of many authors.Chapter three, sufficient conditions are obtained for the positive steady state of the nonautonomous variable delay-Logistic equation to be a global attractor, which extend and improve the results in the known literature.In the last chapter, by using coincide degree theory ,the existences of periodic solution for a kind of differential equation with several delays are obtained.