独特性
锂é纳德方程
数学
极限(数学)
一般化
数学物理
拉普拉斯算子
数学分析
微分方程
纯数学
一阶偏微分方程
精确微分方程
作者
Set Pérez-González,Joan Torregrosa,Pedro J. Torres
标识
DOI:10.1016/j.jmaa.2016.03.004
摘要
The Liénard equation x″+f(x)x′+g(x)=0 appears as a model in many problems of science and engineering. Since the first half of the 20th century, many papers have appeared providing existence and uniqueness conditions for limit cycles of Liénard equations. In this paper we extend some of these results for the case of the generalized φ-Laplacian Liénard equation, (φ(x′))′+f(x)ψ(x′)+g(x)=0. This generalization appears when derivations of the equation different from the classical one are considered. In particular, the relativistic van der Pol equation, (x′/1−(x′/c)2)′+μ(x2−1)x′+x=0, has a unique periodic orbit when μ≠0.
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