Input-output conditions for exponential trichotomy of dynamical systems
Keywords:evolution family, exponential trichotomy, integral equation
AbstractThe aim of the paper is to provide new properties concerning the property of uniform exponential trichotomy on the real line. We obtain a characterization for uniform exponential trichotomy in terms of the solvability of an associated integral equation.
Elaydi, S. and Hájek, O., Exponential trichotomy of differential systems, J. Math. Anal. Appl., 129, pp. 362-374, 1988, https://doi.org/10.1016/0022-247x(88)90255-7
Elaydi, S. and Hájek, O., Exponential dichotomy and trichotomy of nonlinear differential equations, Differ. Integral Equ., 3, pp. 1201-1224, 1990.
Elaydi, S. and Janglajew, K., Dichotomy and trichotomy of difference equations, J. Differ. Equations Appl., 3, pp. 417-448, 1998.
Sacker, R. J. and Sell, G. R., Existence of dichotomies and invariant splittings for linear differential systems III, J. Differential Equations, 22, pp. 497-522, 1976, https://doi.org/10.1016/0022-0396(76)90043-7
Sacker, R. J. and Sell, G. R., Dichotomies for linear evolutionary equations in Banach spaces, J. Differential Equations, 113, pp. 17-67, 1994, https://doi.org/10.1006/jdeq.1994.1113
Sasu, A. L. and Sasu, B., Exponential dichotomy and admissibility for evolution families on the real line, Dynam. Contin. Discrete Impuls. Systems, 13, pp. 1-26, 2006.
Sasu, B. and Sasu, A. L., Input-output conditions for the asymptotic behavior of linear skew-product flows and applications, Comm. Pure Appl. Math., 5, pp. 551-569, 2006, https://doi.org/10.3934/cpaa.2006.5.551
Sasu, B. and Sasu, A. L., Exponential trichotomy and p-admissibility for evolution families on the real line, Math. Z., 253, pp. 515-536, 2006, https://doi.org/10.1007/s00209-005-0920-8
Sasu, A. L. and Sasu, B., Exponential trichotomy for variational difference equations, J. Differ. Equations Appl., in press., https://doi.org/10.1080/10236190802285118
How to Cite
Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory
This work is licensed under a Creative Commons Attribution 4.0 International License.
Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.