Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy
Joint Authors
Kou, Kit Ian
Xia, Yong-Hui
Yuan, Xiaoqing
Wong, Patricia J. Y.
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-05
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
Nonuniform exponential dichotomy has been investigated extensively.
The essential condition of these previous results is based on the assumption that the nonlinear term satisfies |f(t,x)|≤μe−ε|t|.
However, this condition is very restricted.
There are few functions satisfying |f(t,x)|≤μe−ε|t|.
In some sense, this assumption is not reasonable enough.
More suitable assumption should be |f(t,x)|≤μ.
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 |f(t,x)|≤μ.
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.
American Psychological Association (APA)
Xia, Yong-Hui& Yuan, Xiaoqing& Kou, Kit Ian& Wong, Patricia J. Y.. 2014. Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1033963
Modern Language Association (MLA)
Xia, Yong-Hui…[et al.]. Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy. Abstract and Applied Analysis No. 2014 (2014), pp.1-10.
https://search.emarefa.net/detail/BIM-1033963
American Medical Association (AMA)
Xia, Yong-Hui& Yuan, Xiaoqing& Kou, Kit Ian& Wong, Patricia J. Y.. Existence and Uniqueness of Solution for Perturbed Nonautonomous Systems with Nonuniform Exponential Dichotomy. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-10.
https://search.emarefa.net/detail/BIM-1033963
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033963