Periodic solutions and their stability of some higher-order positively homogenous differential equations

被引:3
作者
Cen, Xiuli [1 ]
Llibre, Jaume [2 ]
Zhang, Meirong [3 ]
机构
[1] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China
[2] Univ Autonoma Barcelona, Dept Matemat, Bellaterra 08193, Spain
[3] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China
关键词
Periodic solution; m-Order differential equations; Stability; Averaging theory; SYSTEMS;
D O I
10.1016/j.chaos.2017.11.032
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x((m)) + f(n)(x) = mu h(t), where the integers m, n >= 2, f(n)(x) = delta x(n) or delta vertical bar x vertical bar(n) with delta = +/- 1, h(t) is a continuous T-periodic function of non-zero average, and mu is a positive small parameter. By using the averaging theory, we will give the existence of T-periodic solutions. Moreover, the instability and the linear stability of these periodic solutions will be obtained. (c) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码:285 / 288
页数:4
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