Nonoscillatory and Oscillatory Criteria for First Order Nonlinear Neutral Impulsive Differential Equations

Abstract

A survey of recent studies in neutral impulsive differential equations reveals that most of such works revolve around the quest for oscillatory conditions for linear impulsive differential equations.  The development of oscillatory and nonoscillatory criteria for nonlinear impulsive differential equations has so far attracted very little attention.  In this paper, we obtain sufficient conditions for the existence of oscillatory and nonoscillatory solutions for nonlinear first order neutral impulsive differential equations with constant delays.