Research On Oscillation Of Several Classes Of Differential Equations With Unbounded Delays

This thesis of Master is composed of four chapters, which mainly study some delay and neutral differential equations with unbounded delays. Some oscillation criteria are established.In chapter one, we briefly address the main work of this paper and the background.In chapter two, we study the oscillation of first order unbounded delay differentail equation with positive and negative coefficientsSome sufficient conditions about the oscillation of all solutions of the equation are obtained by use of analytic technique. Our results extend the relevant ones in the literature.Chapter three mainly considers the oscillation of all solutions for first order neutral differentail equations of Euler type with unbounded delaysand first order neutral differentail equations with unbounded delays We give some sufficient conditions for the oscillation of equations, improve and generalize some known results.In chapter four, we investigate the oscillation of first order neutral differential equation of Euler type with unbounded delays We introduce its characteristic equation and establish a sufficient and necessary condition for the oscillation of all sulotions of the equation, moreover, some explicit oscillation results are presented. These results improve and extend some of the existing literature.