Hostname: page-component-54dcc4c588-gwv8j Total loading time: 0 Render date: 2025-09-13T17:00:54.205Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodic Solution of the Caughy Problem

Part of: General theory of linear operators Differential equations in abstract spaces

Published online by Cambridge University Press:  09 April 2009

Trung Dinh Tran
Trung Dinh Tran
Affiliation:
Foundation ProgramQatar UniversityP. O. Box 2713 DohaQatartran@qu.edu.qa
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

MSC classification

Secondary: 47A10: Spectrum, resolvent 47A60: Functional calculus 34G10: Linear equations

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 83 , Issue 3 , December 2007 , pp. 417 - 422
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), 847–857.Google Scholar
[5]Straškraba, I. and Vejvoda, O.. ‘Periodic solutions to abstract differential equations’, Czechoslovak Math. J. 23 (98) (1973), 635–669.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