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Asymptotic equivalence of a linear and nonlinear system with impulse effect

Published online by Cambridge University Press:  20 January 2009

P. S. Simeonov  and
D. D. Bainov
P. S. Simeonov
Affiliation:
Plovdiv University “P. Hilendarski”Plovdiv, Bulgaria
D. D. Bainov
Affiliation:
Plovdiv University “P. Hilendarski”Plovdiv, Bulgaria
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The present paper deals with the problem of asymptotic equivalence of the system with impulse effect

and

where x, y:I→Rn; g:I→Rn; f:I × Rn→Rn; bk:Rn→Rn; I = [0, ∞); Rn is the n-dimensional Euclidean space with a norm |·|; A and B are constant matrices; the moments {tk} constitute an increasing sequence 0 < t1 < … < tk < …, limk→∞tk = ∞.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 1 , February 1988 , pp. 157 - 163
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Brauer, F., Nonlinear differential equations with forcing terms. Proc. Amer. Math. Soc. 15 (1964), 758–765.CrossRefGoogle Scholar
2.Samoilenko, A. M. and Perestjuk, N. A., Stability of the solutions of differential equations with impulse effect, Differentsial'nye Uravneniya 11 (1977), 1981–1992 (in Russian).Google Scholar