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.
International Journal of Dynamical Systems and Differential Equations, 2011 Vol.3 No.1/2, pp.189 - 205
Published online: 09 Feb 2011 *Full-text access for editors Access for subscribers Purchase this article Comment on this article