The existence of periodic solutions for nonlinear systems of first-order differential equations at resonance期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

The existence of periodic solutions for nonlinear systems of first-order differential equations at resonance

Authors:

MA Shi-wang Associate Professor Doctor Wang Zhi-cheng Yu Jian-she

Institution:

(1) Department of Applied Mathematics, Shanghai Jiaotong University, 200030 Shanghai, P R China;(2) Department of Applied Mathematics, Human University, 410082 Changsha, P R China

Abstract:

The nonlinear system of first-order differential equations with a deviating argument

$\dot x(t) = Bx(t) + F(x(t - \tau )) + p(t)$

is considered, where x(t)εR ², τεR, BεR ^2×2, F is bounded and p(t) is continuous and 2π-periodic. Some sufficient conditions for the existence of 2π-periodic solutions of the above equation, in a resonance case, by using the Brouwer degree theory and a continuation theorem based on Mawhin's coincidence degree are obtained. Some applications of the main results to Duffing's equations are also given. Foundation item: the National Natural Science Foundation of China (19801014, 19971026, 19831030) Biography: MA Shi-wang (1965-)

Keywords:

first-order differential equation periodic solution resonance Brouwer degree coincidence degree Duffing equation

本文献已被 CNKI SpringerLink 等数据库收录！

点击此处可从《应用数学和力学(英文版)》浏览原始摘要信息

点击此处可从《应用数学和力学(英文版)》下载免费的PDF全文

设为首页 | 免责声明 | 关于勤云 | 加入收藏