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Remarks on bounded solutions of linear systems

Published online by Cambridge University Press:  17 April 2009

Elena Topuzu  and
Paul Topuzu
Elena Topuzu
Affiliation:
Department of MathematicsWest University of TimişoaraBlv. V. Pârvan 4Timispara 1900România
Paul Topuzu
Affiliation:
Department of MathematicsWest University of TimişoaraBlv. V. Pârvan 4Timispara 1900România
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Abstract

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In the case of continuous time systems with bounded operators (coefficients) the following result, of Perron type is well known: “The linear differential system ẋ = Ax + f(t) has, for every function f continuous and bounded on ℝ, a unique bounded solution on ℝ, if and only if the spectrum of the operator A has no points on the imaginary axis”.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 459 - 467
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Dalecki, J.L. and Krein, M. G., Stability of solutions of differential equations in Banach spaces, translations of Mathematical Monographs, 43 (American Mathematical Society, Providence, R.I., 1974).Google Scholar
[2]Krein, M.G., Lekcii po ustoiqivosti rexenii differencialnyh uravnenii v Banahovom pronstranstve (Kiev, Inst. Mat. DAN SSSR, 1964).Google Scholar
[3]Massera, J.L. and Schäffer, J.J., ‘Linear differential equations and functional Analysis, I’, Ann. of Math. 67 (1958), 517–573.CrossRefGoogle Scholar
[4]Perron, O., ‘Die stabilitätsfrege bei differentialgleichungen’, Math. Z. 32 (1930), 703–728.CrossRefGoogle Scholar
[5]Topuzu, E., ‘On Z-transform and linear discrete time systems’, Lucr. Sem. Mat. Fiz. al I. P. T. (1985), 47–48.Google Scholar
[6]Yosida, K., Functional analysis (Springer-Verlag, Berlin, Heidelberg, New York, 1965).Google Scholar