二阶非线性中立型时滞微分方程的振动性  

Oscillation of Second Order Nonlinear Differential Equations with Neutral Delay

作　　者：仉志余 俞元洪[2] 李淑萍[3] 乔士柱 Zhang Zhiyu;Yu Yuanhong;Li Shuping;Qiao Shizhu(Department of Sciences, Taiyuan Institute of Technology, Taiyuan 030008;Academy of Mathematics and Systems Science, Chinese Academy of Sciences,Beijing 100190;Department of Mathematics, North University of China, Taiyuan 030051)

机构地区：[1]太原工业学院理学系,太原030008 [2]中国科学院数学与系统科学研究院,北京100190 [3]中北大学理学院,太原030051

出　　处：《数学物理学报（A辑）》2019年第4期797-811,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(11701528,11647034);山西省自然科学基金(2011011002-3)~~

摘　　要：该文研究一类二阶非线性中立型时滞微分方程的振动性,利用双Riccati变换和不等式技巧,得到了所研究方程一切解振动的若干新的充分条件.所得结果推广、改进和统一了最近文献中关于半线性、非线性泛函微分方程和广义Emden-Fowler方程的振动定理.同时也给出了主要定理的相应示例.In this paper, the oscillatory behavior of solutions to a nonlinear second-order neutral differential equation is to study. Using double Riccati transformation and the technique of inequations, some new sufficient conditions are obtained for the solutions of all oscillations and the results generalize, improve and unify the oscillation theorems of half linear functional differential equations, nonlinear equations and generalized Emden-Fowler type equations in the literature recently. At last, some examples are given to illustrate the effectiveness of our results.

关 键 词：二阶非线性微分方程 半线性微分方程 EMDEN-FOWLER方程 中立型 RICCATI变换 振动准则 

分 类 号：O175[理学—数学]