高阶泛函微分方程的振动性质

Oscillatory Behavior for High Order Functional Differential Equations

本文借助于Lebesgue测度等工具研究了一类高阶非线性泛函微分方程的振动性质．文中指出．在一定条件下，方程的非振动解仅有两类，而且给出了每一类非振动解存在的必要条件，同时也建立了方程振动的若干充分判据.

In this paper, the osillatory behavior for high order nonlinear functional differential equations are studied by means of the Lebesgue measure. It is found that the nonoscillatory solutions only have two kinds on some conditions. And necessary conditions for the existence of each kind of nonoscillatory solutions are presented as well. At the same time, some sufficient conditions for oscillatory solutions are also established.