A Perron-type theorem for nonautonomous delay equations
Open Mathematics (2013)
- Volume: 11, Issue: 7, page 1283-1295
- ISSN: 2391-5455
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Abstract
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topLuis Barreira, and Claudia Valls. "A Perron-type theorem for nonautonomous delay equations." Open Mathematics 11.7 (2013): 1283-1295. <http://eudml.org/doc/269600>.
@article{LuisBarreira2013,
abstract = {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.},
author = {Luis Barreira, Claudia Valls},
journal = {Open Mathematics},
keywords = {Lyapunov exponents; Nonautonomous delay equations; nonautonomous delay equations},
language = {eng},
number = {7},
pages = {1283-1295},
title = {A Perron-type theorem for nonautonomous delay equations},
url = {http://eudml.org/doc/269600},
volume = {11},
year = {2013},
}
TY - JOUR
AU - Luis Barreira
AU - Claudia Valls
TI - A Perron-type theorem for nonautonomous delay equations
JO - Open Mathematics
PY - 2013
VL - 11
IS - 7
SP - 1283
EP - 1295
AB - 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.
LA - eng
KW - Lyapunov exponents; Nonautonomous delay equations; nonautonomous delay equations
UR - http://eudml.org/doc/269600
ER -
References
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- [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] Zbl1169.34053
- [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] Zbl54.0456.04
- [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]
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