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Uniform asymptotic stability in linear Volterra difference equations. (English) Zbl 0891.39013

The authors study the uniform asymptotic stability of the zero solution of the linear Volterra difference equations of nonconvolution type using the summability of the resolvent matrix. Further, they establish the existence of bounded solutions of nonhomogeneous linear Volterra difference equations. For related results, see the authors’ paper [ibid. 2, No. 4, 401-410 (1996; Zbl 0882.39005)].

MSC:

39A11 Stability of difference equations (MSC2000)

Citations:

Zbl 0882.39005
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References:

[1] DOI: 10.1006/jmaa.1994.1037 · Zbl 0796.39004 · doi:10.1006/jmaa.1994.1037
[2] Elaydi S., An Introduction to Difference Equations (1996) · Zbl 0840.39002 · doi:10.1007/978-1-4757-9168-6
[3] DOI: 10.1080/10236199608808074 · Zbl 0882.39005 · doi:10.1080/10236199608808074
[4] DOI: 10.1016/0022-0396(91)90115-P · Zbl 0722.45003 · doi:10.1016/0022-0396(91)90115-P
[5] DOI: 10.1112/jlms/s2-43.2.305 · Zbl 0728.45007 · doi:10.1112/jlms/s2-43.2.305
[6] Yoshizawa T., Applied Math. Sciences (1975)
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