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Periodic Solution of the Caughy Problem

Published online by Cambridge University Press:  09 April 2009

Trung Dinh Tran
Affiliation:
Foundation ProgramQatar UniversityP. O. Box 2713 [email protected]
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Abstract

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We derive necessary and sufficient conditions for the existence of a time-periodic solution to the abstract Cauchy problem.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2007

References

[1]Daners, D. and Medina, P. K., Abstract Evolution Equations. Periodic Problems and Applications. volume 279 of Pitman Research Notes in Mathematics Series (Longman Scientific & Technical. Harlow. 1992).Google Scholar
[2]Engel, K.-J. and Nagel, R.One-Parameter Semigroupsfor Linear Evolution Equations, volume 194 of Graduate Texts in Mathematics (Springer-Verlag, New York, 2000).Google Scholar
[3]Kato, T., Perturbation Theory for Linear Operators. Die Grundlehren der Mathematischen Wissenschaften. Band 132 (Springer-Verlag, New York, 1966).Google Scholar
[4]Prüss, J., ‘On the spectrum of C 0semigroups’, Trans. Amer. Math. Soc. 284 (1984), 847857.Google Scholar
[5]Straškraba, I. and Vejvoda, O.. ‘Periodic solutions to abstract differential equations’, Czechoslovak Math. J. 23 (98) (1973), 635669.CrossRefGoogle Scholar
[6]Taylor, A. E. and Lay, D. C., Introduction to Functional Analysis. 2nd edition (John Wiley & Sons, New York-Chichester-Brisbane, 1980).Google Scholar