Advances in Dynamical Systems and Applications ISSN 0973-5321, Volume 5, Number 2, pp. 205–214 (2010) http://campus.mst.edu/adsa Leighton–Coles–Wintner Type Oscillation Criteria for Half-Linear Impulsive Differential Equations Abdullah ¨ Ozbekler Atilim University Department of Mathematics 06836 Incek, Ankara, Turkey aozbekler@gmail.com A˘ gacık Zafer Middle East Technical University Department of Mathematics 06531 Ankara, Turkey zafer@metu.edu.tr Abstract In this paper, we obtain new oscillation criteria for second-order half-linear impulsive differential equations having fixed moments of impulse actions. We also generalize the results to nonlinear impulsive equations. The oscillation criteria obtained in this paper can be considered as extensions of those given by Leighton, (J. London Math. Soc. 27 (1952)), Coles (Proc. Amer. Math. Soc. 19 (1968)), and Wintner (Quart. Appl. Math. 7 (1949)). AMS Subject Classifications: 34C10, 34A37. Keywords: Oscillation, half-linear, impulse. 1 Introduction Consider the half-linear impulsive differential equation (r(t)Φ(x ′ )) ′ + q(t)Φ(x)=0, t = θ i ; Δ(r(t)Φ(x ′ )) + q i Φ(x)=0, t = θ i (1.1) where Φ(s) := |s| α−1 s and Δz (t) := z (t + ) − z (t − ), z (t ± ) = lim τ →t ± z (τ ). We assume that (i) α is a real positive constant; (ii) {θ i } is a strictly increasing unbounded sequence of real numbers; {q i } is a real sequence; Received March 31, 2010; Accepted May 6, 2010 Communicated by A. Okay C¸elebi