Existence and uniqueness of solution for perturbed nonautonomous systems with nonuniform exponential dichotomy

• المؤلفون الرئيسيون: Wong, Patricia Jia Yiing, Xia, Yong-Hui, Yuan, Xiaoqing, Kou, Kit Ian
• مؤلفون آخرون: School of Electrical and Electronic Engineering
• التنسيق: مقال
• اللغة: English
• منشور في: 2014
• الموضوعات: DRNTU::Engineering::Electrical and electronic engineering
• الوصول للمادة أونلاين: https://hdl.handle.net/10356/103653; http://hdl.handle.net/10220/20026

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.