Periodic Solutions for a Class of Non-autonomous Newton Differential Equations

被引：1
|
作者：
Llibre, Jaume [1 ]
Makhlouf, Amar [2 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain
[2] Univ Annaba, Dept Math, Elhadjar 23, Annaba, Algeria
来源：
DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2020年 / 28卷 / 02期
关键词：
Periodic solution; Newton differential equation; Averaging theory;
D O I：
10.1007/s12591-016-0333-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide sufficient conditions for the existence of periodic solutions of the second-order non-autonomous differential equation x(sic) = -del V-x(t,x), in R-n, where V(t, x) = parallel to x parallel to(2)/2 + epsilon W + (t, x) with W(t, x) a 2 pi-periodic function in the variable t, epsilon is a small parameter, x is an element of R-n and del V-x((t, x)) = (partial derivative V/partial derivative(x1),...,partial derivative V/partial derivative x(n)). Note that this is a particular class of non-autonomous Newton differential equations. Moreover we provide some applications.
引用
收藏
页码：373 / 379
页数：7
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