Oscillation of second-order dynamic equations

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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)y Δ(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.

Original languageEnglish
Pages (from-to)189-205
Number of pages17
JournalInternational Journal of Dynamical Systems and Differential Equations
Volume3
Issue number1-2
DOIs
StatePublished - 2011

Keywords

  • Dynamic equations
  • Functional equation
  • Oscillation
  • Time scale

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