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