Skip to content

Advertisement

  • Research Article
  • Open Access

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

Advances in Difference Equations20062006:065626

https://doi.org/10.1155/ADE/2006/65626

  • Received: 31 January 2006
  • Accepted: 15 May 2006
  • Published:

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), .

Keywords

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

[123456789101112123456789101112]

Authors’ Affiliations

(1)
Department of Mathematics, Atilim University, Incek-Ankara, 06836, Turkey

References

  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

Copyright

Advertisement