Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy
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...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2014
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| Online Access: | https://hdl.handle.net/10356/103653 http://hdl.handle.net/10220/20026 |
| _version_ | 1811687764596359168 |
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| author | Wong, Patricia Jia Yiing Xia, Yong-Hui Yuan, Xiaoqing Kou, Kit Ian |
| author2 | School of Electrical and Electronic Engineering |
| author_facet | School of Electrical and Electronic Engineering Wong, Patricia Jia Yiing Xia, Yong-Hui Yuan, Xiaoqing Kou, Kit Ian |
| author_sort | Wong, Patricia Jia Yiing |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T05:21:30Z |
| format | Journal Article |
| id | ntu-10356/103653 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:21:30Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1036532020-03-07T14:00:37Z Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy Wong, Patricia Jia Yiing Xia, Yong-Hui Yuan, Xiaoqing Kou, Kit Ian School of Electrical and Electronic Engineering DRNTU::Engineering::Electrical and electronic engineering 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. Published version 2014-07-03T02:36:21Z 2019-12-06T21:17:07Z 2014-07-03T02:36:21Z 2019-12-06T21:17:07Z 2014 2014 Journal Article 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-. 1085-3375 https://hdl.handle.net/10356/103653 http://hdl.handle.net/10220/20026 10.1155/2014/725098 en Abstract and applied analysis © 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. application/pdf |
| spellingShingle | DRNTU::Engineering::Electrical and electronic engineering Wong, Patricia Jia Yiing Xia, Yong-Hui Yuan, Xiaoqing Kou, Kit Ian Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy |
| title | Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy |
| title_full | Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy |
| title_fullStr | Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy |
| title_full_unstemmed | Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy |
| title_short | Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy |
| title_sort | existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy |
| topic | DRNTU::Engineering::Electrical and electronic engineering |
| url | https://hdl.handle.net/10356/103653 http://hdl.handle.net/10220/20026 |
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