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

Xiuli Cen; Jaume Llibre; Meirong Zhang

doi:10.1016/j.chaos.2017.11.032

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

Xiuli Cen, Jaume Llibre, Meirong Zhang

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

2 Citations (Scopus)

Abstract

© 2017 Elsevier Ltd In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x(m)+fn(x)=μh(t),where the integers m, n ≥ 2, fn(x)=δxn or δ|x|n with δ=±1, h(t) is a continuous T-periodic function of non-zero average, and μ 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.

Original language	English
Pages (from-to)	285-288
Journal	Chaos, Solitons and Fractals
Volume	106
DOIs	https://doi.org/10.1016/j.chaos.2017.11.032
Publication status	Published - 1 Jan 2018

Keywords

Averaging theory
Periodic solution
Stability
m-Order differential equations

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title = "Periodic solutions and their stability of some higher-order positively homogenous differential equations",

abstract = "{\textcopyright} 2017 Elsevier Ltd In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x(m)+fn(x)=μh(t),where the integers m, n ≥ 2, fn(x)=δxn or δ|x|n with δ=±1, h(t) is a continuous T-periodic function of non-zero average, and μ 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.",

keywords = "Averaging theory, Periodic solution, Stability, m-Order differential equations",

author = "Xiuli Cen and Jaume Llibre and Meirong Zhang",

year = "2018",

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doi = "10.1016/j.chaos.2017.11.032",

language = "English",

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TY - JOUR

T1 - Periodic solutions and their stability of some higher-order positively homogenous differential equations

AU - Cen, Xiuli

AU - Llibre, Jaume

AU - Zhang, Meirong

PY - 2018/1/1

Y1 - 2018/1/1

N2 - © 2017 Elsevier Ltd In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x(m)+fn(x)=μh(t),where the integers m, n ≥ 2, fn(x)=δxn or δ|x|n with δ=±1, h(t) is a continuous T-periodic function of non-zero average, and μ 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.

AB - © 2017 Elsevier Ltd In the present paper we study periodic solutions and their stability of the m-order differential equations of the form x(m)+fn(x)=μh(t),where the integers m, n ≥ 2, fn(x)=δxn or δ|x|n with δ=±1, h(t) is a continuous T-periodic function of non-zero average, and μ 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.

KW - Averaging theory

KW - Periodic solution

KW - Stability

KW - m-Order differential equations

U2 - 10.1016/j.chaos.2017.11.032

DO - 10.1016/j.chaos.2017.11.032

M3 - Article

VL - 106

SP - 285

EP - 288

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -