On the asymptotic behaviour of the solutions of a second order linear differential equation with small damping
On the asymptotic behaviour of the solutions of a second order linear differential equation with small damping
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小阻尼二阶线性微分方程解的渐近行为
DOI：
10.1007/bf01872105
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发表时间：
1993
影响因子：
0.9
通讯作者：
J. Karsai
中科院分区：
文献类型：
--
作者：
J. Karsai
本文考虑线性微分方程（1）~+ a（t）~+ x= 0，其中函数a（t）非负且分段连续。寻找保证方程（1）的每一个解在t~ c~时趋于零的条件的经典问题，已经成为方程（1）的大量出版物[3]-[8]的主题，最近也成为更一般的非线性方程的主题。存在相当尖锐的充分条件，但是尖锐性问题，即找到必要和充分条件，甚至对于线性方程（1）也没有解决。这个问题是我们论文的主题。
In this paper we consider the linear differential equation (1)~+ a (t)~+ x= 0, where the function a (t) is supposed to be nonnegative and piecewise continuous. The classical problem of finding conditions guaranteeing that every solution of (1) tends to zero as t~ c~, has been the subject of a great number of publications [3]-[8] for equation (1) and recently also for more general nonlinear equations. There are rather sharp sufficient conditions, but the sharpness problem, that is to find necessary and sufficient conditions, has not been solved even for the linear equation (1). This problem is the subject of our paper.