Oscillation criteria of second-order half-linear dynamic equations on time scales
type: Item
instance of: scholarly article
title: Oscillation criteria of second-order half-linear dynamic equations on time scales
zbMATH Open document ID: 1082.34032
published in: Journal of Computational and Applied Mathematics
publication date: 2005-05-04T00:00:00Z
review text: The subject of the paper is oscillation of solutions of second-order delta differential equations of the type \[ (p(t)(x^\Delta(t))^\gamma)^\Delta+q(t)x^\gamma(t)=0\tag{1} \] on quite general time scales. Here, \(\gamma>1\) is an odd positive integer and \(p,\;q\) are positive right-dense continuous functions. The function \((1/p)^{1/ \gamma}\) may be integrable (in the sense of time scale analysis) at \(+\infty\) or not. Sufficient conditions for the oscillatory character of all non-trivial solutions of (1) are given in both cases. The main theorems are applicable, in particular, to half-linear difference equations and half-linear ordinary differential equations, unifying and extending previous results. At the end of the paper, some examples are discussed to illustrate the range of applicability of the main results.
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 39A12
zbMATH DE Number: 2164840
zbMATH Keywords: oscillation
zbMATH Keywords: second-order half-linear dynamic equations
zbMATH Keywords: time scale
author: S. H. Saker
MaRDI profile type: Publication
full work available at URL: j.cam.2004.09.028
OpenAlex ID: W2073680172
cites work: Dynamic equations on time scales: A survey
cites work: Oscillation results for a dynamic equation on a time scale
cites work: Oscillation Properties of an Emden-Fowler Type Equation on Discrete Time Scales
cites work: Q2723195
cites work: Q4797834
cites work: Oscillation of second order nonlinear dynamic equations on time scales
cites work: Oscillation criteria for perturbed nonlinear dynamic equations
cites work: A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales
cites work: Q4811360
cites work: Positive solutions for a nonlinear differential equation on a measure chain
cites work: Riccati equations on a measure chain
cites work: Oscillation criteria for second-order matrix dynamic equations on a time scale
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: On a disconjugacy criterion for second-order dynamic equations on time scales
cites work: Analysis on measure chains - a unified approach to continuous and discrete calculus
cites work: Q4167008
cites work: Oscillation of an Euler-Cauchy dynamic equation
cites work: Oscillation of nonlinear dynamic equations on time scales.
cites work: Oscillation and comparison theorems for half-linear second-order difference equations
DOI: 10.1016/J.CAM.2004.09.028
description: scientific article; zbMATH DE number 2164840