一类三阶非线性中立型分布时滞微分方程的振动性  

On the Oscillation of Certain Third-order Nonlinear Neutral Differential Equations with Distributed Delay

作　　者：王世利[1] 仉志余[2] 

机构地区：[1]中北大学数学系,山西太原030051 [2]太原工业学院理学系,山西太原030008

出　　处：《数学的实践与认识》2015年第13期278-285,共8页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(2011011002-3)

摘　　要：研究一类三阶非线性中立型分布时滞微分方程的振动性.利用算子和积分技巧分别给出了不存在引理中提到的i)型正解和ii)型正解的判定条件,进而借助适当的比较定理,建立了判别该类方程振动的若干新的充分条件,所得定理推广和改进了最近文献中的若干结果.结果充分反映了时滞在方程振动中的影响作用.A certain kind of oscillation of the third order nonlinear neutral delay differential equation is studied in this paper. By using the operator and the integrating skills, we give the judging criteria of the （i） type positive solution and （ii） type positive solution mentioned ＇in the inexistence lemma, then some new sufficient conditions judging the sort of oscillation of equations are established with the help of appropriate comparison theorems, the theorems obtained promote and improve some conclusions in some latest literatures, the results response the effect of the delay in the oscillation of equations. Then we give some concrete examples to illustrate these main conclusions.

关 键 词：三阶泛函微分方程 中立型 非线性 振动准则 

分 类 号：O175[理学—数学]