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. In this paper, we consider an impulsive differential equation with continuous and piecewise constant arguments of the form 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. x $^{′}$( t ) + a ( t ) x ( t ) + b ( t ) x ( t − τ ) + c ( t ) x ([ t − 1]) = 0 , t = t$_{i}$, t ≥ t$_{0}$ > 0 , (1) Δ x ( t$_{i}$ ) = b$_{i}$x ( t$_{i}$ ) , i = 1 , 2 , ..., (2) 1. Introduction arXiv:1603.01030v1 [math.CA] 3 Mar 2016 $^{1}$Corresponding Author: fkarakoc@ankara.edu.tr Phone: +90(312)2126720 Fax: +90(312)2235000 1