Analysis On Qualitative Properties Of Solutions For Two Classes Of Differential Equations

This dissertation is concerned with qualitative properties of solutions for two classes of differential equations. The existence of periodic solutions for three-order p-Laplacian neutral differential equations is obtained, and the oscillation of solutions for nonlinear fractional differential equations is given. This dissertation is divided into three chapters, and the main contents are as follows.In the first chapter, the basic information of p-Laplacian neutral differential equa-tion and the research status on oscillation of solutions for differential equation are briefly reviewed. Further more, the main results of this dissertation are summarized.In Chapter2, based on the coincidence degree theory, some sufficient conditions for existence of T-periodic solutions for three-order p-Laplacian neutral functional differential equation are obtained, which generalizes and improves the results of the existing literature.Finally, by using generalized Riccati transformation, inequalities and integration av-erage technique and some properties of Riemann-Liouville derivative, the oscillation of solutions for nonlinear fractional differential equation is established. In addition, an ex-ample is given to demonstrate the results.