A Perron-type theorem for nonautonomous delay equations

• Autorzy: Luis Barreira , Claudia Valls
• Języki publikacji: EN

Abstrakty

EN

We show that if the Lyapunov exponents of a linear delay equation x′ = L(t)x t are limits, then the same happens with the exponential growth rates of the solutions to the equation x′ = L(t)x t + f(t, x t) for any sufficiently small perturbation f.

Słowa kluczowe

EN

Lyapunov exponents; Nonautonomous delay equations

Kategorie tematyczne

• 34D10: Perturbations
• 34D08: Characteristic and Lyapunov exponents

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 7
• Strony: 1283-1295

Daty

wydano

2013-07-01

online

2013-04-26

Twórcy

autor

Luis Barreira

• Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisboa, Portugal

autor

Claudia Valls

• Departamento de Matemática, Instituto Superior Técnico, 1049-001, Lisboa, Portugal

Bibliografia

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• [2] Barreira L., Valls C., Stability of Nonautonomous Differential Equations, Lecture Notes in Math., 1926, Springer, Berlin, 2008
• [3] Coffman C.V., Asymptotic behavior of solutions of ordinary difference equations, Trans. Amer. Math. Soc., 1964, 110, 22–51 http://dx.doi.org/10.1090/S0002-9947-1964-0156122-9[Crossref]
• [4] Coppel W.A., Stability and Asymptotic Behavior of Differential Equations, D.C. Heath, Boston, 1965
• [5] Hale J.K., Verduyn Lunel S.M., Introduction to Functional-Differential Equations, Appl. Math. Sci., 99, Springer, New York, 1993
• [6] Hartman P., Wintner A., Asymptotic integrations of linear differential equations, Amer. J. Math., 1955, 77, 45–86 http://dx.doi.org/10.2307/2372422[Crossref]
• [7] Lettenmeyer F., Über das asymptotische Verhalten der Lösungen von Differentialgleichungen und Differentialgleichungssystemen, Sitzungsberichte der Königl. Bayerischen Akademie der Wissenschaften, München, 1929, 201–252
• [8] Matsui K., Matsunaga H., Murakami S., Perron type theorem for functional differential equations with infinite delay in a Banach space, Nonlinear Anal., 2008, 69(11), 3821–3837 http://dx.doi.org/10.1016/j.na.2007.10.017[Crossref]
• [9] Perron O., Über Stabilität und asymptotisches Verhalten der Integrale von Differentialgleichungssystemen, Math. Z., 1929, 29(1), 129–160 http://dx.doi.org/10.1007/BF01180524[Crossref]
• [10] Pituk M., A Perron type theorem for functional differential equations, J. Math. Anal. Appl., 2006, 316(1), 24–41 http://dx.doi.org/10.1016/j.jmaa.2005.04.027[Crossref]
• [11] Pituk M., Asymptotic behavior and oscillation of functional differential equations, J. Math. Anal. Appl., 2006, 322(2), 1140–1158 http://dx.doi.org/10.1016/j.jmaa.2005.09.081[Crossref]

Identyfikatory

DOI

10.2478/s11533-013-0244-6