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Abstract Samah Saad Mahmoud Euat Tallah. On the oscillation and non-oscillation of solutions of linear and nonlinear differential equations. Philosophy degree of science dissertation of Pure Mathematics (Ph. D), University College for Women, Ain Shams University. The main purpose of thesis is to study; discuss the oscillation and non-oscillation of solutions of linear and non-linear of differential equations. Also, we study different classes of impulsive second order differential equations. Finally, we discuss the oscillation of first order neutral differential equation under impulse effect. Our analysis is based on Riccati transformations and the integral average technique. Applications are provided to illustrate our results obtained in the case of impulse or without impulse effect. |