一类次线性中立型时滞微分方程的渐近性质  

Asymptotic properties of a class of delay differential equations with a sub-linear neutral term

作　　者：韩忠月[1] 俞元洪[2] HAN Zhongyue;YU Yuanhong(School of Mathematics and Big Data,Dezhou University,Dezhou Shandong 253023,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]德州学院数学与大数据学院,山东德州253023 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《华东师范大学学报（自然科学版）》2021年第1期1-7,共7页Journal of East China Normal University(Natural Science)

基　　金：山东省自然科学基金(ZR2017LA012)。

摘　　要：运用广义Riccati变换和中值定理,讨论了具有阻尼项的次线性中立型时滞微分方程的振动性及渐近性质.就参数γ与β的大小关系和条件∫^(∞)t0(1/R(t))1/γdt=∞的交叉结合在方程振动性的作用方面做了分析,得到了该方程存在振动解的充分条件,推广和改进了已有结果,并用实例给出了其应用.This paper studies the oscillation and asymptotic properties of delay differential equations with damping and sub-linear neutral terms using the generalized Riccati transformation technique and the mean value theorem. After analyzing the function of the cross-link between the condition∫^(∞)t0(1/R(t))1/γdt=∞ and the relationship of parameters and in the differential equations oscillation, the sufficient conditions for the existence of vibration solutions are provided to extend the existing results in the cited literature. Lastly,some applications are given to illustrate the significance of these results.

关 键 词：阻尼项 时滞 次线性中立型 微分方程 振动性 

分 类 号：O175.12[理学—数学]