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# Oscillation of a Class of Impulsive Differential Equations with Continuous and Piecewise Constant Arguments 

Fatma KARAKOC ¸ 1 

Department of Mathematics, Faculty of Sciences, Ankara University, Turkey 

Abstract A class of first order linear impulsive differential equation with continuous and piecewise constant arguments is studied. Sufficient conditions for the oscillation of the solutions are obtained. 

Keywords : Oscillation; Delay; Piecewise constant argument; impulse. 

AMS Subject Classification: 34K11, 34K45. 

## 1. Introduction 

In this paper, we consider an impulsive differential equation with continuous and piecewise constant arguments of the form 

<img src='content_image/314940.jpg'>

<img src='content_image/314941.jpg'>

where a ∈ C ([0 , ∞ ) , R ) , b, c ∈ C ([0 , ∞ ) , [0 , ∞ )), τ ∈ R + is a fixed constant, [ . ] denotes the greatest integer function, { t$_{i}$ } is a sequence of real numbers such that 0 < t$_{0}$ < t$_{1}$ < t$_{2}$ < ... < t$_{j}$ < t$_{j}$$_{+1}$ < ..., and lim i $_{→∞}$t$_{i}$ = ∞ , Δ x ( t$_{i}$ ) = x ( t + i ) − x ( t − i ) , x ( t + i ) = lim t → t + i x ( t ) , x ( t − i ) = lim t → t − i x ( t ) , b$_{i}$ ̸ = 1, i = 1 , 2 , ..., are constants. 

