A Perturbation Result for Bounded Solutions of Linear Differential Systems under the Integrable Dichotomy Condition

Article Sidebar

PDF
Published: Mar 30, 2018
Keywords:
Bounded solutions, Differential systems, Integrable dichotomy, Perturbation

Main Article Content

Parinya Sa Ngiamsunthorn*
Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand

Abstract

The aim of this paper is to study the behavior of bounded solutions of linear differential systems under perturbation. We show that if the unperturbed linear differential system has an integrable dichotomy then the perturbed system has a unique bounded solution which converges to the bounded solution of the unperturbed linear differential system when the perturbation is sufficiently small.


Keywords: Bounded solutions, Differential systems, Integrable dichotomy, Perturbation


E-mail: parinya.san@kmutt.ac.th

Article Details

How to Cite
Ngiamsunthorn*, P. S. (2018). A Perturbation Result for Bounded Solutions of Linear Differential Systems under the Integrable Dichotomy Condition. CURRENT APPLIED SCIENCE AND TECHNOLOGY, 12(2), 96–100. retrieved from https://li01.tci-thaijo.org/index.php/cast/article/view/135715
Issue
Vol. 12 No. 2 (2012)
Section
Original Research Articles

Copyright Agreement Statement

The corresponding author has to submit Copyright Agreement form after the article is accepted for publication in order to warrant that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.

 

The author(s) grant Current Applied Science and Technology a non-exclusive, irrevocable, royalty-free license to publish, reproduce, distribute, and archive the article in print and electronic form with effect if and when the article is accepted for publication. In the event that the article is withdrawn prior to acceptance or is declined, this agreement shall have no effect, and no party shall be bound by it.

 

The author(s) retain copyright of this article, including but not limited to the right to reproduce and distribute the article, to include it in a thesis or book, and to post it on an institutional or personal repository, provided that the original publication in Current Applied Science and Technology is properly cited.

 

 

 

References

[1] Baroun, M., Boulite, S., Diagana,T. and Maniar, L., 2009. Almost periodic solutions to some semilinear non-autonomous thermoelastic plate equations. J. Math. Anal. Appl., 349, 74-84.
[2] Henry, D., 1981. Geometric theory of semilinear parabolic equations. Berlin: Springer-Verlag.
[3] Prüss, J., 1984. On the spectrum of C0-semigroups, Trans. Amer. Math. Soc., 284(2), 847-857.
[4] Pinto, M., 2010. Dichotomy and existence of periodic solutions of quasilinear functional differential equations, Nonlinear Analysis, 72, 1227-1234.
[5] Barreira, L. and Valls, C., 2008. Stability of nonautonomous differential equations. Berlin Heidelberg: Springer-Verlag.