Title: Oscillation of second-order dynamic equations

Authors: Raegan Higgins

Addresses: Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA

Abstract: In this paper, we consider the second-order nonlinear dynamic equations (p(t)yΔ(t))Δ + q(t)f(y(τ(t))) = 0 and (p(t)yΔ(t))Δ + q(t)f(yσ (t)) = 0 on an isolated time scale T. Our first goal is to establish a relationship between the oscillatory behaviour of these equations. Here we assume that τ : 𝕋 → 𝕋. We also give two results about the behaviour of the linear form of the latter equation on a general time scale that is unbounded above. We use the Riccati transformation technique to obtain our results.

Keywords: oscillation; second-order dynamic equations; time scales; functional equations; nonlinear dynamic equations; Riccati transformation.

DOI: 10.1504/IJDSDE.2011.038502

International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.1/2, pp.189 - 205

Published online: 24 Jan 2015 *

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