一类微分方程零解全局弱吸引和全局吸引到充要条件

数学物理学报 ›› 2009, Vol. 29 ›› Issue (3): 529-537.

• 论文 • 下一篇

一类微分方程零解全局弱吸引和全局吸引到充要条件

赵丽琴

(北京师范大学数学科学学院,数学与复杂系统教育部重点实验室北京100875)

收稿日期:2007-03-07 修回日期:2008-10-11 出版日期:2009-06-25 发布日期:2009-06-25
基金资助:
国家自然科学基金(10671020)资助

Necessary and Sufficient Conditions for the Global Weak Attractivity and Global Attractivity of a Class of Nonlinear Differential Equations

ZHAO Li-qin

(School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing 100875)

Received:2007-03-07 Revised:2008-10-11 Online:2009-06-25 Published:2009-06-25
Supported by:
国家自然科学基金(10671020)资助

摘要/Abstract

摘要：

考虑二阶微分方程
x = φ(y)-F(x), y=- g(x)q(y)
零解的全局弱吸引和全局吸引性, 说明了Filippov条件(A₂) 不能排除最大椭圆扇形S^* 的存在性, 也不能排除∂S^*作为其外侧邻域轨线正向极限集的可能. 全面回答了文献[8]末提出的问题;得到了方程(E)满足或不满足Filippov 条件时零解全局弱吸引和全局吸引的一系列充分必要条件, 同时也得到了零解全局渐近稳定的一些新条件.

关键词: Filippov条件, 全局吸引, 全局弱吸引, 全局渐近稳定

Abstract:

This paper deals with the global weak attractivity and global attractivity for the nonlinear differential equations
x = φ（y）-F(x), {y}=- g(x)q(y).
It is shown that Filippov condition (A₂) cannot exclude the existence of the maximum elliptic sector S^* and it cannot exclude the possibility of ∂S^* as the ω-limit set of the orbits departing from the exterior of S^*. The problem proposed by Jiang Jifa in Nonlinear Analysis, 28(5), 855--870(1997) is answered by a negative answer. A series of necessary and sufficient conditions for the global weak attractivity and global attractivity are established for both the cases that Filippov condition holds and Filippov condition fails. Some new conditions for the global asymptotic stability are also obtained.

Key words: Filippov condition, Global attractivity, Global , weak , attractivity, Global , asymptotic stability

中图分类号:

34D05

赵丽琴. 一类微分方程零解全局弱吸引和全局吸引到充要条件[J]. 数学物理学报, 2009, 29(3): 529-537.

ZHAO Li-Qin. Necessary and Sufficient Conditions for the Global Weak Attractivity and Global Attractivity of a Class of Nonlinear Differential Equations[J]. Acta mathematica scientia,Series A, 2009, 29(3): 529-537.

参考文献

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一类微分方程零解全局弱吸引和全局吸引到充要条件

Necessary and Sufficient Conditions for the Global Weak Attractivity and Global Attractivity of a Class of Nonlinear Differential Equations

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