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Title: Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy
Authors: Wong, Patricia Jia Yiing
Xia, Yong-Hui
Yuan, Xiaoqing
Kou, Kit Ian
Keywords: DRNTU::Engineering::Electrical and electronic engineering
Issue Date: 2014
Source: Xia, Y.-H., Yuan, X., Kou, K. I., & Wong, P. J. Y. (2014). Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy. Abstract and Applied Analysis, 2014, 725098-.
Series/Report no.: Abstract and applied analysis
Abstract: Nonuniform exponential dichotomy has been investigated extensively. The essential condition of these previous results is based on the assumption that the nonlinear term satisfies . However, this condition is very restricted. There are few functions satisfying . In some sense, this assumption is not reasonable enough. More suitable assumption should be . To the best of the authors' knowledge, there is no paper considering the existence and uniqueness of solution to the perturbed nonautonomous system with a relatively conservative assumption . In this paper, we prove that if the nonlinear term is bounded, the perturbed nonautonomous system with nonuniform exponential dichotomy has a unique solution. The technique employed to prove Theorem 4 is the highlight of this paper.
ISSN: 1085-3375
DOI: 10.1155/2014/725098
Rights: © 2014 Yong-Hui Xia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:EEE Journal Articles

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