Skip to main content


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

  • 890 Accesses

  • 18 Citations


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), .



  1. 1.

    Agarwal RP, Bohner M, Saker SH: Oscillation of second order delay dynamic equations. to appear in The Canadian Applied Mathematics Quarterly

  2. 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.2004.06.041

  3. 3.

    Bohner M, Peterson A: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser Boston, Massachusetts; 2001:x+358.

  4. 4.

    Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348.

  5. 5.

    Erbe LH, Zhang BG: Oscillation of discrete analogues of delay equations. Differential and Integral Equations 1989,2(3):300–309.

  6. 6.

    Hilger S: Ein Maßkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten, M.S. thesis. Universität Würzburg, Würzburg; 1988.

  7. 7.

    Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results in Mathematics 1990,18(1–2):18–56.

  8. 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.

  9. 9.

    Şahiner Y: Oscillation of second-order delay differential equations on time scales. Nonlinear Analysis 2005,63(5–7):e1073-e1080.

  10. 10.

    Şahiner Y, Stavroulakis IP: Oscillations of first order delay dynamic equations. to appear in Dynamic Systems and Applications

  11. 11.

    Zhang BG, Deng X: Oscillation of delay differential equations on time scales. Mathematical and Computer Modelling 2002,36(11–13):1307–1318.

  12. 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.2004.04.038

Download references

Author information

Correspondence to Y Şahİner.

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and Permissions

About this article

Cite this article

Şahİner, Y. Oscillation of second-order neutral delay and mixed-type dynamic equations on time scales. Adv Differ Equ 2006, 065626 (2006) doi:10.1155/ADE/2006/65626

Download citation


  • Differential Equation
  • Partial Differential Equation
  • Ordinary Differential Equation
  • Functional Analysis
  • Functional Equation