Oscillation and nonoscillation of solutions of second order linear differential equations with integrable coefficients
Oscillation and nonoscillation of solutions of second order linear differential equations with integrable coefficients
复制标题
具有可积系数的二阶线性微分方程解的振荡和非振荡
DOI：
10.1090/s0002-9947-1969-0251305-6
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发表时间：
1969
影响因子：
1.3
通讯作者：
J. Wong
中科院分区：
文献类型：
--
作者：
J. Wong
(1) x ' ' +a(t)x = 0, t >，其中a(t)是t的局部可积函数。如果(1)的所有解在[0,0]上有任意大的零，我们称方程(1)为振荡的，否则，我们称方程(1)为非振荡的。根据Sturm分离定理[21]，如果(1)的一个解是振荡的，则所有解都是振荡的。对于(1)的非振荡也是如此。关于二阶线性振荡的文献是大量的。第一个这样的结果当然是斯特姆的经典定理，它断言
(1) x"+a(t)x = 0, t > 0, where a(t) is a locally integrable function of t. We call equation (1) oscillatory if all solutions of (1) have arbitrarily large zeros on [0, oo), otherwise, we say equation (1) is nonoscillatory. As a consequence of Sturm's Separation Theorem [21], if one of the solutions of (1) is oscillatory, then all of them are. The same is true for the nonoscillation of (1). The literature on second order linear oscillation is voluminous. The first such result is of course the classical theorem of Sturm which asserts that