Skip to main content

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

Abstract

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), .

[123456789101112123456789101112]

References

  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

    MathSciNet  Article  MATH  Google Scholar 

  3. 3.

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

    Book  MATH  Google Scholar 

  4. 4.

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

    MATH  Google Scholar 

  5. 5.

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

    MathSciNet  MATH  Google Scholar 

  6. 6.

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

    MATH  Google Scholar 

  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.

    MathSciNet  Article  MATH  Google Scholar 

  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.

    MathSciNet  Article  MATH  Google Scholar 

  9. 9.

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

    MATH  Google Scholar 

  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.

    MathSciNet  Article  MATH  Google Scholar 

  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

    MathSciNet  Article  MATH  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

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 (https://creativecommons.org/licenses/by/2.0), 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). https://doi.org/10.1155/ADE/2006/65626

Download citation

Keywords

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