Anderson, Douglas R.; Krueger, Robert J.; Peterson, Allan C. Delay dynamic equations with stability. (English) Zbl 1134.39011 Adv. Difference Equ. 2006, Article ID 94051, 19 p. (2006). Summary: We first give conditions which guarantee that every solution of a first-order linear delay dynamic equation for isolated time scales vanishes at infinity. Several interesting examples are given. In the last half of the paper, we give conditions under which the trivial solution of a nonlinear delay dynamic equation is asymptotically stable, for arbitrary time scales. Cited in 12 Documents MSC: 39A12 Discrete version of topics in analysis 39A11 Stability of difference equations (MSC2000) Keywords:asymptotic stability; first-order linear delay dynamic equation; time scales PDFBibTeX XMLCite \textit{D. R. Anderson} et al., Adv. Difference Equ. 2006, Article ID 94051, 19 p. (2006; Zbl 1134.39011) Full Text: DOI EuDML References: [1] Bohner M, Peterson AC: Dynamic Equations on Time Scales. An Introduction with Applications. Birkhäuser Boston, Massachusetts; 2001:x+358. · Zbl 0978.39001 · doi:10.1007/978-1-4612-0201-1 [2] Bohner M, Peterson AC (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348. · Zbl 1025.34001 [3] Haddock JR, Kuang Y: Asymptotic theory for a class of nonautonomous delay differential equations.Journal of Mathematical Analysis and Applications 1992,168(1):147-162. 10.1016/0022-247X(92)90195-J · Zbl 0764.45005 · doi:10.1016/0022-247X(92)90195-J [4] Hilger S: Analysis on measure chains—a unified approach to continuous and discrete calculus.Results in Mathematics 1990,18(1-2):18-56. · Zbl 0722.39001 · doi:10.1007/BF03323153 [5] Kac V, Cheung P: Quantum Calculus, Universitext. Springer, New York; 2002:x+112. · Zbl 0986.05001 · doi:10.1007/978-1-4613-0071-7 [6] Kelley WG, Peterson AC: The Theory of Differential Equations, Classical and Qualitative. Pearson Prentice Hall, New Jersey; 2004. [7] Kuang Y: Delay Differential Equations with Applications in Population Dynamics, Mathematics in Science and Engineering. Volume 191. Academic Press, Massachusetts; 1993:xii+398. · Zbl 0777.34002 [8] Ladde GS, Lakshmikantham V, Zhang BG: Oscillation Theory of Differential Equations with Deviating Arguments, Monographs and Textbooks in Pure and Applied Mathematics. Volume 110. Marcel Dekker, New York; 1987:vi+308. · Zbl 0832.34071 [9] Raffoul Y: Stability and Periodicity in Completely Delayed Equations. to appear in Journal of Mathematical Analysis and Applications · Zbl 1115.39015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.