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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

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