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

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

How to Cite

Citation Format

Ngiamsunthorn*, P. S. . (2018). A Perturbation Result for Bounded Solutions of Linear Differential Systems under the Integrable Dichotomy Condition. CURRENT APPLIED SCIENCE AND TECHNOLOGY, 96-100.

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.

Author Information

Parinya Sa Ngiamsunthorn*

Department of Mathematics, King Mongkut’s University of Technology Thonburi, Bangkok, Thailand

About this Article

Journal

Vol. 12 No. 2 (2012)

Type of Manuscript

Original Research Article

Keywords

Bounded solutions, Differential systems, Integrable dichotomy, Perturbation

Published

30 March 2018

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

Abstract

How to Cite

References

Author Information

Parinya Sa Ngiamsunthorn*

About this Article

Journal

Type of Manuscript

Keywords

Published

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