一类二阶变系数微分方程基本解组的渐近逼近式与解的渐近性态

Asymptotic Form of the Solution of a Class of Second Ordinary Differential Equations

根据常微分方程渐近解理论分别获得了二阶线性变系数齐次常微分方程在两组不同条件下的基本解组的渐近逼近式,证明了该方程在两组不同条件下所有解有界和零解全局渐近稳定.实例验证了本文所述方法的有效性.

This paper studies the asymptotic form of the basic solutions to the equation x ＋ a（ t）x ＋ b（ t）x =0 under the two different conditions and it proves the boundness of all solutions and the global asymptotic stability of the zero solution to the equation x ＋ a（t） x ＋ b（t）x = 0. The examples show that the methods offered in this paper are efficient.