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Uniform asymptotic stability in nonlinear Volterra discrete systems. (English) Zbl 1051.39003

The authors employ the notion of total stability to obtain new criteria for uniform asymptotic stability of the zero solution of a nonlinear Volterra discrete system. The main results are discrete analogs of those obtained by B. Zhang [Funkc. Ekvacioj, Ser. Int. 40, No. 3, 335–351 (1997; Zbl 0897.45009)].

MSC:

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

Citations:

Zbl 0897.45009
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References:

[1] Hino, Y.; Murakami, S., Total stability and uniform asymptotic stability for linear Volterra equations, J. London Math. Soc., 43, 305-312 (1991) · Zbl 0728.45007
[2] Hino, Y.; Murakami, S., Stabilities in linear integrodifferential equations, (Lecture Notes in Numerical and Applied Analysis, Volume 15 (1996), Kinokuniya: Kinokuniya Tokyo), 31-46 · Zbl 0848.45003
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[9] Raffoul, Y., Boundedness and periodicity of Volterra systems of difference equations, Journal of Difference Equations, 4, 381-393 (1998) · Zbl 0912.39006
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