一类二阶中立型微分方程的振动和非振动准则

Oscillation and Non-oscillation Criteria for a Class of Second Order Neutral Differential Equations

中立型泛函微分方程的振动性在理论和应用中有着重要意义.研究了一类具有正负系数的二阶非线性中立型时滞泛函微分方程的振动性,利用Banach空间的不动点原理,通过引入参数函数并结合一些分析技巧,获得了该类方程存在非振动解的新的准则,并同时得到了该类方程振动的判别准则,这些准则改善了对方程的条件限制,所得结论推广并改进了现有文献中的一系列结果.

The oscillation theory of neutral functional differential equations plays an important role in both theory and application.This paper discusses oscillation of a class of second order nonlinear neutral delay functional differential equation with positive and negative coefficients.Using the fixed point theorem in Banach space,and by introducing parameter function and certain analytic techniques,some new non-oscillation criteria for the equation are obtained.In addition,some sufficient conditions for oscillation of the equation are proposed.These criteria can improve the restriction of the conditions for the equation.Some existed results in the literatures are further improved and extended.