Periodic Solutions of Second-Order Differential Equations with Large Parameters

被引：0

作者：

V. V. Sazonov

A. V. Troitskaya

机构：

[1] Keldysh Institute of Applied Mathematics of RAS,

[2] Moscow State University,undefined

来源：

Mechanics of Solids | 2018年 / 53卷

关键词：

second-order differential equations; large parameter; periodic solutions; Poincaré method; Lichtenstein method;

D O I：

暂无

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学科分类号：

摘要：

A second-order differential equation containing a large parameter is considered. Such an equation can be interpreted as an equation of constrained oscillations of a mechanical system with one degree of freedom, provided that the fundamental frequency of the system substantially exceeds the external frequency. We provide a new proof of the existence of a periodic solution of that equation such that it is close to the periodic solution of the corresponding degenerate equation. That proof is obtained by means of the Poincaré method.

引用

页码：87 / 94

页数：7