一类具阻尼项的三阶非线性中立型泛函微分方程的振动性和渐近性  

Oscillatory and asymptotic behavior of third-order nonlinear neutral functional differential equations with damping terms

作　　者：曾云辉 罗李平 汪志红 汪安宁 俞元洪[3] ZENG Yunhui;LUO Liping;WANG Zhihong;WANG Anning;YU Yuanhong(College of Mathematics and Statistics,Hengyang Normal University,Hengyang 421002,China;Hunan Provincial Key Laboratory of Intelligent Information Processing and Application,Hengyang 421002,China;Academy of System Sciences,Chinese Academy of Science,Beijing 100190,China)

机构地区：[1]衡阳师范学院数学与统计学院,湖南衡阳421002 [2]智能信息处理与应用湖南省重点实验室,湖南衡阳421002 [3]中国科学院数学与系统科学研究院,北京100190

出　　处：《振动与冲击》2021年第8期19-27,共9页Journal of Vibration and Shock

基　　金：湖南省自然科学基金项目(2019JJ40004);湖南省教育厅科学基金重点项目(20A063);湖南省大学生创新创业训练计划项目(S201910546030,S201912659001,201912659004);湖南省双一流应用特色学科项目(湘教通[2018]469);湖南省科技创新计划项目(2016TP1020);衡阳师范学院智能信息处理与应用湖南省重点实验室开放基金项目(IIPA19K07)。

摘　　要：研究一类具阻尼项的三阶非线性中立型连续分布时滞泛函微分方程解的振动性和渐近性,利用广义Riccati变换、积分平均技巧和一些分析技巧,对α≠β的情况,建立了一组保证该方程每一解振动或者收敛到零的充分条件,所得结果改进和推广了最新文献中的一些熟知的准则。The objective of this paper is to investigates oscillatory and asymptotic behaviors of solutions of a class of third-order nonlinear neutral differential equations with continuously delay and damping terms.By using generalized Riccati transformations,integral averaging technique and some necessary technique,a set of new sufficient conditions was set forα≠βwhich ensure that every solution of the equations oscillates or converges to zero.The results improve and extend related criteria in recent literature.

关 键 词：阻尼项 渐近性 三阶中立型微分方程 广义Riccati变换 

分 类 号：O175.27[理学—数学]