Oscillation of second-order dynamic equations

Raegan Higgins

doi:10.1504/IJDSDE.2011.038502

Oscillation of second-order dynamic equations

Raegan Higgins

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we consider the second-order nonlinear dynamic equations (p(t)y^Δ(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 language	English
Pages (from-to)	189-205
Number of pages	17
Journal	International Journal of Dynamical Systems and Differential Equations
Volume	3
Issue number	1-2
DOIs	https://doi.org/10.1504/IJDSDE.2011.038502
State	Published - 2011

Keywords

Dynamic equations
Functional equation
Oscillation
Time scale

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title = "Oscillation of second-order dynamic equations",

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.",

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AB - 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.

KW - Dynamic equations

KW - Functional equation

KW - Oscillation

KW - Time scale

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JO - International Journal of Dynamical Systems and Differential Equations

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