具无界中立系数的三阶Emden-Fowler微分方程的弱振动性  

Weak oscillation of third-order Emden-Fowler neutral differential equations with unbounded neutral coefficients

作　　者：曾云辉 汪安宁 汪志红 罗李平 ZENG Yunhui;WANG Anning;WANG Zhihong;LUO Liping(College of Mathematics and Statistics,Hengyang Normal University,Hengyang 421002,China;Department of Mathematics and Computational Science,Nanyue College of Hengyang Normal University,Hengyang 421008,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]衡阳师范学院南岳学院数学与计算科学系,湖南衡阳421008

出　　处：《中山大学学报（自然科学版）（中英文）》2021年第6期169-179,共11页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：湖南省自然科学基金(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,S202112659007,201912659004);湖南省双一流应用特色学科项目(湘教通[2018]469);湖南省重点实验室项目(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(IIPA19K07)。

摘　　要：研究一类具有无界中立系数的三阶Emden-Fowler微分方程解的弱振动性。通过引入参数函数和广义Riccati变换,运用积分平均技术和一些分析技巧,获得了方程所有解弱振动的几个新的振动准则,所得结果推广和完善了最近文献中的一些结果。The weak oscillation of solutions of third-order Emden-Fowler differential equations with unbounded neutral coefficients is studied.By introducing parameter function and the generalized Riccati transformations,using integral averaging technique and some necessary technique,some new oscillation criteria which ensure that all solutions of the studied equation weakly oscillates are obtained.The results generalize and perfect a number of related results in the literature recently.

关 键 词：三阶 Emden-Fowler微分方程 弱振动性 非振动性 

分 类 号：O175.27[理学—数学]