Oscillation criteria for second-order nonlinear delay dynamic equations
type: Item
instance of: scholarly article
title: Oscillation criteria for second-order nonlinear delay dynamic equations
zbMATH Open document ID: 1125.34046
published in: Journal of Mathematical Analysis and Applications
publication date: 2007-06-26T00:00:00Z
review text: The authors consider the second-order nonlinear delay dynamic equation \[ \left(r(t)x^\Delta(t)\right)^\Delta +p(t)f(x(\tau(t))=0 \] on a time scale. By employing a generalized Riccati transformation of the form \[ w(t):= \delta(t)\left[\frac{r(t)x^\Delta(t)}{x(t)} +r(t)a(t)\right], \] they establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. The obtained results improve the well-known oscillation results for dynamic equations and include as special cases the oscillation results for differential equations. Some applications to special time scales \(R, N, q^{N_{0}}\) with \(q>1\) and four examples are also included to illustrate the main results.
Mathematics Subject Classification ID: 34K11
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 5167530
zbMATH Keywords: Second-order nonlinear delay dynamic equation
zbMATH Keywords: Time scales
zbMATH Keywords: Oscillation
zbMATH Keywords: Generalized Riccati technique
author: Lynn Erbe
author: Allan Peterson
author: S. H. Saker
reviewed by: Qiru Wang
MaRDI profile type: Publication
full work available at URL: j.jmaa.2006.10.055
OpenAlex ID: W2024303336
cites work: Dynamic equations on time scales: A survey
cites work: Q5423054
cites work: Oscillation criteria for second-order nonlinear neutral delay dynamic equations
cites work: Oscillation criteria for nonlinear perturbed dynamic equations of second-order on time scales
cites work: Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations
cites work: Q2723195
cites work: Oscillation of second order nonlinear dynamic equations on time scales
cites work: Oscillation criteria for perturbed nonlinear dynamic equations
cites work: Q4811360
cites work: Riccati equations on a measure chain
cites work: Boundedness and oscillation for nonlinear dynamic equations on a time scale
cites work: OSCILLATION CRITERIA FOR SECOND-ORDER NONLINEAR DYNAMIC EQUATIONS ON TIME SCALES
cites work: Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales
cites work: Q5487681
cites work: Analysis on measure chains - a unified approach to continuous and discrete calculus
cites work: Q3434027
cites work: Oscillation of nonlinear dynamic equations on time scales.
cites work: Oscillation criteria of second-order half-linear dynamic equations on time scales
cites work: Boundedness of solutions of second-order forced nonlinear dynamic equations
cites work: Oscillation of second-order forced nonlinear dynamic equations on time scales
cites work: Oscillation of second-order delay differential equations on time scales
cites work: Oscillation of second-order nonlinear delay dynamic equations on time scales
DOI: 10.1016/J.JMAA.2006.10.055
description: scientific article; zbMATH DE number 5167530