Boundedness and vanishing of solutions for a forced delay dynamic equation
Advances in Difference Equations volume 2006, Article number: 035063 (2006)
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.
Anderson DR: Asymptotic behavior of solutions for neutral delay dynamic equations on time scales. Advances in Difference Equations 2006, 2006: 11 pages.
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 5
Anderson DR, Krueger RJ, Peterson AC: Delay dynamic equations with stability. Advances in Difference Equations 2006, 2006: 19 pages.
Bohner M, Peterson A: Dynamic Equations on Time Scales, An Introduction with Applications. Birkhäuser Boston, Massachusetts; 2001:x+358.
Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348.
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. 10.1080/10236199508808016
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-Q
Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus. Results in Mathematics 1990,18(1–2):18–56.
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.
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)00179-7
Kulenović MRS, Merino O: Discrete Dynamical Systems and Difference Equations with Mathematica. Chapman & Hall/CRC, Florida; 2002:xvi+344.
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.1999.6325
Qian C, Sun Y: Global attractivity of solutions of nonlinear delay differential equations with a forcing term. to appear in Nonlinear Analysis
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.2005.01.017
About this article
Cite this article
Anderson, D.R. Boundedness and vanishing of solutions for a forced delay dynamic equation. Adv Differ Equ 2006, 035063 (2006). https://doi.org/10.1155/ADE/2006/35063