Periodic orbits of a non-autonomous quadratic differential system obtained from third-order differential equations

Jaume Llibre; Amar Makhlouf

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Periodic orbits of a non-autonomous quadratic differential system obtained from third-order differential equations

机译：由三阶微分方程获得的非自治二次微分系统的周期轨道

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摘要

We provide sufficient conditions for the existence of periodic solutions of the third-order differential equations u'" + (a_1u + a_0)u" + (b_1u + b_0)u' + c_2u~2 + a_0b_0u = ε~2F(t, u, u', u", ε), where a_0, a_1, b_0, b_1, c_2 are real arbitrary parameters with b_0 > 0, e is a small parameter and F is a 2π/(b_0)~(1/2)-periodic nonlinear function in the variable t. The prime denotes derivative with respect to the independent variable t. Moreover we provide an application.

机译：我们为三阶微分方程u'“ +（a_1u + a_0）u” +（b_1u + b_0）u'+ c_2u〜2 + a_0b_0u =ε〜2F（t，u）的周期解的存在提供了充分的条件。，u'，u“，ε），其中a_0，a_1，b_0，b_1，c_2是b_0> 0的实数任意参数，e是小参数，F是2π/（b_0）〜（1/2）-变量t中的周期非线性函数。素数表示相对于自变量t的导数。此外，我们提供了一个应用。

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来源
《Dynamical Systems》 |2012年第2期|p.161-168|共8页
作者
Jaume Llibre; Amar Makhlouf;
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作者单位

Departament de Matematiques, Universilat Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia, Spain;

Department of Mathematics, University of Annaba, Elhadjar 23 Annaba, Algeria;

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原文格式 PDF
正文语种 eng
中图分类
关键词
periodic orbit; third-order differential equation; quadratic system; averaging theory;

机译：周期性轨道三阶微分方程;二次系统平均理论;

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1. Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation [J] . Jaume Llibre, Ammar Makhlouf Differential equations and dynamical systems . 2019,第1a3期

机译：从三阶微分方程获得的差分方程二次系统的零跳周期轨道
2. Time-periodic measures, random periodic orbits, and the linear response for dissipative non-autonomous stochastic differential equations [J] . Micha? Branicki, Kenneth Uda Research in the Mathematical Sciences . 2021,第3期

机译：时间周期措施，随机周期轨道和耗散非自主随机微分方程的线性响应
3. Existence of Periodic Solutions and Bounded Invariant Sets for Non-Autonomous Third-Order Differential Equations [J] . O. Rabiei Motlagh, Z. Afsharnezhad Vietnam journal of mathematics . 2003,第3期

机译：非自治三阶微分方程周期解和有界不变集的存在
4. On the Stabilizing Solution of Periodic Riccati Differential Equations Related to a Class of Stochastic Linear Quadratic Differential Game [C] . V. Dragan, S. Aberkane, I. Ivanov, IFAC World Congress . 2018

机译：关于一类随机线性二次差分比赛的周期性中Riccati微分方程的稳定解
5. Evolution systems of measures for non-autonomous stochastic differential equations with Lévy noise [D] . Wooster, Robert, III 2009

机译：具有Lévy噪声的非自治随机微分方程测度的演化系统
6. Application of Laplace–Adomian Decomposition Method for the Analytical Solution of Third-Order Dispersive Fractional Partial Differential Equations [O] . Rasool Shah, Hassan Khan, Muhammad Arif, 2019

机译：拉普拉斯 - adomian分解方法在三阶分散分数偏微分方程分析解的应用
7. Periodic orbits of a non-autonomous quadratic differential system obtained from third-order differential equations [O] . Llibre Jaume 2012

机译：由三阶微分方程获得的非自治二次微分系统的周期轨道
8. PART I Recent Work on Families of Periodic Solutions of Ordinary Differential Equations. PART II Singular Solutions of Systems of Real Analytic Equations. PART III The Stromgren-Wintner Principle on the Termination of Families of Periodic Solutions. [R] . Daniel C. Lewis 1959

机译：第一部分关于常微分方程周期解族的近期研究。第二部分实分析方程组的奇异解。第三部分stromgren-Wintner关于终止家庭周期解的原则。

Periodic orbits of a non-autonomous quadratic differential system obtained from third-order differential equations

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