Existence, uniqueness and conditional stability of periodic solutions to evolution equations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:433

Article

Nguyen Thieu Huy¹  Ngo Quy Dang² 

[1] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, Hanoi, Vietnam

[2] Thai Binh Teacher Training Coll, Quang Trung, Thai Binh, Vietnam

关键词: Evolution equations;    Periodic solutions;    Conditional stability;    Exponential dichotomy;   

DOI  :  10.1016/j.jmaa.2015.07.059

来源: Elsevier

【 摘 要 】

Using an ergodic approach, we investigate the condition for existence and uniqueness of periodic solutions to linear evolution equation u = A(t)u f(t), t >= 0, and to semi-linear evolution equations of the form u = A(t)u g(u)(t), where the operator-valued function t -> (t) and the vector-valued function f(t) are T-periodic, and Nemytskii's operator g is locally Lipschitz and maps T-periodic functions to T-periodic functions. We then apply the results to study the existence, uniqueness, and conditional stability of periodic solutions to the above semi-linear equation in the case that the family (A(t))t>0 generates an evolution family having an exponential dichotomy. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free