摘要
二阶常微分方程解的振动性是常微中熟知的一个研究课题，不论在理论上还是在应用上都是很重要的研究项目，在这方面至少有几百篇文献。近来具有时滞的二阶微分方程解的振动性已有不少工作，有的讨论常时滞，即二阶微分差分方程解的振动性，有的讨论变时滞的情况，也就是二阶泛函微分方程解的振动性，最近，关于时超类型的二阶泛函微分方程解的振动性的研究也已有初步的成果。
In this paper, we consider oscillation and nonoscillation of the solutions for the more general second-order functional differential eguations. Some sufficient conditions which keep all the solutions oscillating were obtained.Here is an example for the eguationyw(t) + f(t),y(t), y((?)(t)), y'(t), y'(h(t))=0, t≥A≥O (5) where (?)(t)→∞, h(t)→∞ as t→∞.Theorem 1. Besides the conditions on the continuity and the existence and unigueness of solution, we suppose that the following conditions are also satisfied:(i) f(t,u,v,w,z) have the same sign as u, v, if u, v have the same sign;(ii) for every positive monotonu nondecreasing function or negative nonincreasing function, The following eguation f(t,y(t),y(g(t)),y'(h(t)))dt=∞·sgny is correct.Thenall the solutions of equation (5) oscillate.The theorems contain partial results of the articles[2] [3] .The necessary and sufficient conditions in which eg (5) has a nonosillatory bounded solution are established in this paper. This is theorem 3.In presant paper, We proved five theorems which contain some results of the foreign articles.
