First Order Delay Differential Equations

CHAPTER 2

2.1. Introduction

In this chapter, we will describe some of the recent developments in oscillation theory of first order delay differential equations. This theory is interesting from the theoretical as well as the practical point of view. It is well known that homogeneous ordinary differential equations (ODEs) of first order do not possess oscillatory solutions. But the presence of deviating arguments can cause oscillation of solutions. In this chapter we will see these phenomena and we will show various techniques used in oscillation and nonoscillation theory of differential equations with delays. We will present some criteria for oscillation and for the existence of positive solutions of delay differential equations of first order.