New Oscillation Ciriteria of First Order Delay Differential Equations

Abstract

Abstract. In this paper we shall consider the first order delay differential equations with variable coefficients. Some new sufficient conditions for oscillation of all solutions axe obtained. Our results based on the analysis of the generalized charachterestic equation. The results partially improve some previously known results in the literature. Some examples are considered to illustrate our main results. IntroductionIn recent years there has been much research activity concerning the oscillatory behavior of solutions of delay differential equations. To a large extent, this is due to the fact that, the delay differential equations are important in applications. New applications which involve delay differential equations continue to arise with increasing frequency in the modelling of diverse phenomena in Physics In this paper we shall consider the following first delay differential equation,