Open Access

Boundedness and vanishing of solutions for a forced delay dynamic equation

Advances in Difference Equations20062006:035063

DOI: 10.1155/ADE/2006/35063

Received: 30 March 2006

Accepted: 14 July 2006

Published: 17 October 2006

Abstract

We give conditions under which all solutions of a time-scale first-order nonlinear variable-delay dynamic equation with forcing term are bounded and vanish at infinity, for arbitrary time scales that are unbounded above. A nontrivial example illustrating an application of the results is provided.

[1234567891011121314]

Authors’ Affiliations

(1)
Department of Mathematics and Computer Science, Concordia College

References

  1. Anderson DR: Asymptotic behavior of solutions for neutral delay dynamic equations on time scales. Advances in Difference Equations 2006, 2006: 11 pages.Google Scholar
  2. Anderson DR, Hoffacker J: Positive periodic time-scale solutions for functional dynamic equations. The Australian Journal of Mathematical Analysis and Applications 2006,3(1):1–14. article 5MathSciNetMATHGoogle Scholar
  3. Anderson DR, Krueger RJ, Peterson AC: Delay dynamic equations with stability. Advances in Difference Equations 2006, 2006: 19 pages.MathSciNetMATHGoogle Scholar
  4. Bohner M, Peterson A: Dynamic Equations on Time Scales, An Introduction with Applications. Birkhäuser Boston, Massachusetts; 2001:x+358.View ArticleMATHGoogle Scholar
  5. Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348.MATHGoogle Scholar
  6. Erbe LH, Xia H, Yu JS: Global stability of a linear nonautonomous delay difference equation. Journal of Difference Equations and Applications 1995,1(2):151–161. 10.1080/10236199508808016MathSciNetView ArticleMATHGoogle Scholar
  7. Gopalsamy K, Kulenović MRS, Ladas G: Environmental periodicity and time delays in a "food-limited" population model. Journal of Mathematical Analysis and Applications 1990,147(2):545–555. 10.1016/0022-247X(90)90369-QMathSciNetView ArticleMATHGoogle Scholar
  8. 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
  9. Kocić VL, Ladas G: Global Behavior of Nonlinear Difference Equations of Higher Order with Applications, Mathematics and Its Applications. Volume 256. Kluwer Academic, Dordrecht; 1993:xii+228.MATHGoogle Scholar
  10. Kong Q, Sun Y, Zhang B: Nonoscillation of a class of neutral differential equations. Computers & Mathematics with Applications 2002,44(5–6):643–654. 10.1016/S0898-1221(02)00179-7MathSciNetView ArticleMATHGoogle Scholar
  11. Kulenović MRS, Merino O: Discrete Dynamical Systems and Difference Equations with Mathematica. Chapman & Hall/CRC, Florida; 2002:xvi+344.View ArticleMATHGoogle Scholar
  12. Matsunaga H, Miyazaki R, Hara T: Global attractivity results for nonlinear delay differential equations. Journal of Mathematical Analysis and Applications 1999,234(1):77–90. 10.1006/jmaa.1999.6325MathSciNetView ArticleMATHGoogle Scholar
  13. Qian C, Sun Y: Global attractivity of solutions of nonlinear delay differential equations with a forcing term. to appear in Nonlinear AnalysisGoogle Scholar
  14. Zhang X, Yan J: Global asymptotic behavior of nonlinear difference equations. Computers & Mathematics with Applications 2005,49(9–10):1335–1345. 10.1016/j.camwa.2005.01.017MathSciNetView ArticleMATHGoogle Scholar

Copyright

© Douglas R. Anderson. 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.