Open Access

Oscillation of second-order neutral delay and mixed-type dynamic equations on time scales

Advances in Difference Equations20062006:065626

Received: 31 January 2006

Accepted: 15 May 2006

Published: 9 July 2006


We consider the equation (r(t)(yΔ(t)) γ )Δ + f(t, x(δ(t))) = 0, , where y(t) = x(t) + p(t)x(τ(t)) and γ is a quotient of positive odd integers. We present some sufficient conditions for neutral delay and mixed-type dynamic equations to be oscillatory, depending on deviating arguments τ(t) and δ(t), .


Authors’ Affiliations

Department of Mathematics, Atilim University


  1. Agarwal RP, Bohner M, Saker SH: Oscillation of second order delay dynamic equations. to appear in The Canadian Applied Mathematics QuarterlyGoogle Scholar
  2. Agarwal RP, O'Regan D, Saker SH: Oscillation criteria for second-order nonlinear neutral delay dynamic equations. Journal of Mathematical Analysis and Applications 2004,300(1):203–217. 10.1016/j.jmaa.2004.06.041MathSciNetView ArticleMATHGoogle Scholar
  3. Bohner M, Peterson A: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser Boston, Massachusetts; 2001:x+358.View ArticleMATHGoogle Scholar
  4. Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348.MATHGoogle Scholar
  5. Erbe LH, Zhang BG: Oscillation of discrete analogues of delay equations. Differential and Integral Equations 1989,2(3):300–309.MathSciNetMATHGoogle Scholar
  6. Hilger S: Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, M.S. thesis. Universität Würzburg, Würzburg; 1988.MATHGoogle Scholar
  7. Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results in Mathematics 1990,18(1–2):18–56.MathSciNetView ArticleMATHGoogle Scholar
  8. Ladas G, Philos ChG, Sficas YG: Sharp conditions for the oscillation of delay difference equations. Journal of Applied Mathematics and Simulation 1989,2(2):101–111.MathSciNetView ArticleMATHGoogle Scholar
  9. Şahiner Y: Oscillation of second-order delay differential equations on time scales. Nonlinear Analysis 2005,63(5–7):e1073-e1080.MATHGoogle Scholar
  10. Şahiner Y, Stavroulakis IP: Oscillations of first order delay dynamic equations. to appear in Dynamic Systems and ApplicationsGoogle Scholar
  11. Zhang BG, Deng X: Oscillation of delay differential equations on time scales. Mathematical and Computer Modelling 2002,36(11–13):1307–1318.MathSciNetView ArticleMATHGoogle Scholar
  12. Zhang BG, Shanliang Z: Oscillation of second-order nonlinear delay dynamic equations on time scales. Computers & Mathematics with Applications 2005,49(4):599–609. 10.1016/j.camwa.2004.04.038MathSciNetView ArticleMATHGoogle Scholar


© Y. Şahİner 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.