Oscillation of first order differential equations

Differential equations has been studied for a long time and its applications are avaliable in many scientific branches. In many years there has been much research activity concerning the oscillaton of delay differential equations. In the first chapter of the thesis, we tread some results given for differential equations in the literature. In the second chapter, general defination and some theorems for oscillation of delay differential equations are given. In the third chapter, conditions for oscillations of autonomous and non-autonomous differential equation have been examined and, techniques to analyze the generalized characteristic equations to obtain some infinite integral conditions for oscillation of the non-autonomous delay differential equations have been introduced. In the fourth chapter, we have examined some integral conditions for the oscillations of all solutions of nonlinear first order neutral delay differential equations and, sufficient conditions for the existence of a positive solution of the neutral delay differential equations.