具无界中立系数的三阶非线性微分方程解的振动性和渐近性  

Oscillatory and asymptotic behavior of third-order nonlinear neutral differential equations with unbounded neutral coefficients

作　　者：曾云辉 汪志红 汪安宁 罗李平 俞元洪[2] ZENG Yunhui;WANG Zhihong;WANG Anning;LUO Liping;YU Yuanhong(College of Mathematics and Statistics,Hengyang Normal University,Hengyang 421008,Hunan Province,China;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,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421008 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《浙江大学学报（理学版）》2021年第1期46-56,共11页Journal of Zhejiang University（Science Edition）

基　　金：湖南省双一流应用特色学科资助项目(湘教通[2018]469);湖南省重点实验室资助项目(2016TP1020);湖南省教育厅科学基金重点项目(20A063);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);湖南省自然科学基金资助项目(2019JJ4004);湖南省大学生创新创业训练计划资助项目(S201910546030,S201912659001,201912659004).

摘　　要：研究了具无界中立系数的三阶非线性微分方程解的振动性和渐近性。通过引入参数函数和广义Riccati变换,结合微分不等式、积分平均等技巧,给出了方程每个解振动或收敛于零的若干新的充分条件,这些结果很容易被推广至更一般的中立型微分方程和时标上的中立型动力方程,最后用例子进行了说明。The objective of this paper is to study oscillatory and asymptotic behaviors of solutions of third-order nonlinear neutral differential equations with unbounded neutral coefficients.By introducing the parameter function and the generalized Riccati transformations,and jointly applying the differential inequality technique and integral averaging technique,we establish some new sufficient conditions which ensure that every solution of the equations oscillates or converges to zero.The results obtained can be easily extended to more general neutral differential equations as well as neutral dynamic equations on the scales.An example is provided to illustrate new results.

关 键 词：三阶 中立型微分方程 渐近性 非振动性 

分 类 号：O175.26[理学—基础数学]