ON THE PERIODIC SOLUTIONS OF A CLASS OF DUFFING DIFFERENTIAL EQUATION

被引：7

作者：

Llibre, Jaume ^{[1
]}

Roberto, Luci Any ^{[2
]}

机构：

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

[2] Ibilce UNESP, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, Brazil

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2013年 / 33卷 / 01期

关键词：

Periodic solution; averaging method; Duffing differential equation; bifurcation; stability; STABILITY;

D O I：

10.3934/dcds.2013.33.277

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we study the periodic solutions, their stability and bifurcation for the class of Duffing differential equation x '' + epsilon Cx' + epsilon(2) A(t)x + b(t)x(3) = epsilon(3) Lambda h(t), where C > 0, epsilon > 0 and Lambda are real parameter, A(t), b(t) and h(t) are continuous T-periodic functions and epsilon is sufficiently small. Our results are proved using the averaging method of first order.

引用

页码：277 / 282

页数：6

共 6 条

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[2] Stability and exact multiplicity of periodic solutions of duffing equations with cubic nonlinearities [J].

Chen, Hongbin ;

Li, Yi .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (12) :3925-3932

[3]

Duffing G., 1918, ERZWUNGEN SCHWINGUNG, V41

[4]

Mawhin J., 1997, EQ BRNO P, V9, P115

[5]

ORTEGA R, 1989, B UNIONE MAT ITAL, V3B, P533

[6]

Verhulst F., 1991, Nonlinear Differential Equations and Dynamical Systems

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