Periodic Solutions of Continuous Third-Order Differential Equations with Piecewise Polynomial Nonlinearities

被引：0

作者：

Llibre, J. ^{[1
]}

Lopes, B. D. ^{[2
]}

de Moraes, J. R. ^{[3
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain

[2] Univ Fed ABC, Ctr Matemat Comp & Cognicao, BR-09210170 Santo Andre, SP, Brazil

[3] Univ Estadual Mato Grosso do Sul, Curso Matemat, BR-79804970 Dourados, MS, Brazil

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2020年 / 30卷 / 11期

基金：

欧盟地平线“2020”;

关键词：

Periodic solution; averaging method; third-order differential equation; piecewise differential equation; LIMIT-CYCLES; SYSTEMS;

D O I：

10.1142/S0218127420501588

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider third-order autonomous continuous piecewise differential equations in the variable x. For such differential equations with nonlinearities of the form x(m), we investigate their periodic solutions using the averaging theory. We remark that since the differential system is only continuous we cannot apply to it the classical averaging theory, that needs that the differential system be at least of class C-2.

引用

页数：7

共 50 条

[1] Periodic solutions of some classes of continuous third-order differential equations
Amar, Makhlouf
Djamel, Debbabi
CHAOS SOLITONS & FRACTALS, 2017, 94 : 112 - 118
[2] POSITIVE PERIODIC SOLUTIONS FOR THIRD-ORDER NONLINEAR DIFFERENTIAL EQUATIONS
Ren, Jingli
Siegmund, Stefan
Chen, Yueli
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2011,
[3] Multiplicity of Periodic Solutions for Third-Order Nonlinear Differential Equations
Yang, Xuxin
Wang, Weibing
Lv, Dingyang
MATHEMATICAL PROBLEMS IN ENGINEERING, 2015, 2015
[4] ON ALMOST PERIODIC SOLUTIONS TO THIRD-ORDER NEUTRAL DELAY-DIFFERENTIAL EQUATIONS WITH PIECEWISE CONSTANT ARGUMENT
Rongkun Zhuang
Hongwu Wu
Annals of Differential Equations, 2013, 29 (01) : 114 - 120
[5] ASYMPTOTIC BEHAVIOUR OF SOLUTIONS OF THIRD-ORDER DIFFERENTIAL EQUATIONS WITH RAPIDLY VARYING NONLINEARITIES
Evtukhov, Vyacheslav M.
Sharay, Natalia, V
MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2019, 77 : 43 - 57
[6] Periodic solutions of third-order functional differential equations with variable coefficients
Zhengqiu Z.
Zhicheng W.
Applied Mathematics-A Journal of Chinese Universities, 2002, 17 (2) : 145 - 154
[7] PERIODIC SOLUTIONS OF THIRD-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS
Zhang Zhengqiu Wang ZhichengDept.ofAppl.Math.
AppliedMathematics:AJournalofChineseUniversities, 2002, (02) : 145 - 154
[8] Positive periodic solutions for fully third-order ordinary differential equations
Li, Yongxiang
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (11) : 3464 - 3471
[9] Existence of Periodic Solutions for Nonlinear Fully Third-Order Differential Equations
Zhang, Yunfei
Pei, Minghe
JOURNAL OF FUNCTION SPACES, 2020, 2020
[10] EXISTENCE OF POSITIVE PERIODIC SOLUTIONS TO THIRD-ORDER DELAY DIFFERENTIAL EQUATIONS
Gui, Zhanji
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2006,

← 1 2 3 4 5 →