A SPECIAL KIND OF NONOSCILLATORY SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS

In this note the nonoscillatory property of y"+p(x)y=0,where p(x) is a periodic pulse function,is considered.Sufficient condition for guaranteeing nonscillation is obtained.We compare the result with obtained by applying Adamov's theorem.     

二阶线性方程边值问题解的变号性质

一、引言 我们研究的是边值问题的解在[0,1]上的变号次数。其中q(x),f(x)。在[0,1]上连续,a,a′β,β′保证(1),(2)的解存在[1]。主要结果是当q(x)≤π~2-d,d>0时。(1),(2)的解u(x)在[0,1]上变号的次数最多不超过f(x)在[0,1]上变号的次数加两次变号,即线性系统因外力引起的响应函数的震荡次数不超过外力振荡次数与固有振荡次数之和。