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Delay dynamic equations with stability. (English) Zbl 1134.39011

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.

MSC:

39A12 Discrete version of topics in analysis
39A11 Stability of difference equations (MSC2000)
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References:

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