临界状态下一阶时滞微分方程的线性化振动性  

Linearized Oscillations for First Order Delay Differential Equations in a Critical State

作　　者：唐先华[1] 庾建设[2] 王志成[2] 

机构地区：[1]中南工业大学应用数学与应用软件系,湖南长沙410083 [2]湖南大学应用数学系,湖南长沙410082

出　　处：《数学学报（中文版）》2000年第2期349-358,共10页Acta Mathematica Sinica：Chinese Series

基　　金：高校博士点基金!1997007

摘　　要：本文首先在临界状态下建立了一阶非线性非自治时滞微分方程ｘ＇（ｔ）＋＝１ｐｉｘ（ｔ－Ｔｉ）＋ｆ（ｔ，ｘ（ｔ－σ１（ｔ））…，ｘ（ｔ－σｎ（ｔ））＝０与一个相关的二阶常微分方程振动性等价定理，进而给出了一阶非线性自治微分方程与相应的线性方程振动性等价的充分条件，从而较好地回答了张炳根在文［２］中提出的一个公开问题．We establish an equivalent theorem of oscillation of the following first order nonlinear delay differential equation x'(t) and a related second order ordinary differential equation in a critical state. And then we obtain some sufficient conditions which guarantee the first order nonlinear nonautonomous differential equation and the corresponding linear equation have the same oscillatory behavior. A open problem proposed by Zhang is solved.

关 键 词：时滞微分方程 临界状态 线性化振动性 常微方程 

分 类 号：O175.13[理学—数学]