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Asymptotic equivalence of ordinary and operator-differential equations

Published online by Cambridge University Press:  17 April 2009

P. S. Simeonov  and
D. D. Bainov
P. S. Simeonov
Affiliation:
23, Oborishte Str., 1504 Sofia, Bulgaria.
D. D. Bainov
Affiliation:
23, Oborishte Str., 1504 Sofia, Bulgaria.
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Abstract

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The paper considers problems connected with the asymptotic equivalence of the system of ordinary differential equations

and the system of operator differential equations

The generality of the operator At guarantees a number of its important implementations. By a specific choice of the operator At the system (2) can be one of the concentrated delay, a system of distributed delay, a system with maxima, etcetera.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 35 , Issue 3 , June 1987 , pp. 415 - 425
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Fennell, R.E. and Proctor, T.G., “On asymptotic behavior of perturbed nonlinear systems”, Proc Amer. Math. Soc. 31 (1972), 499–504.Google Scholar
[2]Marlin, J.A. and Struble, R.A., “Asymptotic equivalence of nonlinear systems”, J. Differential Equations 6 (1969), 578–596.CrossRefGoogle Scholar