一类带有分段常数变元的线性时滞微分方程的振动判据  

Oscillation criterions of a class of linear delay differential equations with piecewise constant arguments

作　　者：张冰清 寇春海[1] ZHANG Bingqing;KOU Chunhai(College of Science,Donghua University,Shanghai,China;Song Jiang High School Affiliated to ECUPL,Shanghai,China)

机构地区：[1]东华大学理学院,上海 [2]华东政法大学附属松江高级中学,上海

出　　处：《东华大学学报（自然科学版）》2024年第2期170-180,共11页Journal of Donghua University(Natural Science)

基　　金：上海市自然科学基金(19ZR1400500)。

摘　　要：针对一类带有分段变元的线性时滞微分方程,在系数缓慢变化的情形下,利用Bolzano-Weierstrass定理,建立判定其振动性的充分条件,将已有的下极限型条件改进为上极限型条件,进而可以判定部分原先所不能判定的方程的振动性,并采用2个例子证明其有效性。This paper deals with a class of linear delay differential equations with piecewise arguments.In the cases of slowly varying coefficients,some sufficient conditions are obtained to conclude the oscillation of all solutions for the related equations by employing Bolzano-Weierstrass theorem.These results improve the lower limit type criteria in the existing literature to the upper limit type criteria,and then the oscillation of some equations that can not be concluded before can be concluded.Two examples are given to illustrate the effectiveness of the established results.

关 键 词：线性时滞微分方程 分段常数变元 振动 

分 类 号：O175.12[理学—数学]