一类具非线性中立项的二阶微分方程的振动性  

Oscillation of certain second-order differential equations with nonlinear neutral term

作　　者：覃桂茳 杨甲山[1,3] 刘玉周 QIN Guijiang;YANG Jiashan;LIU Yuzhou(School of Data Science and Software Engineering,Wuzhou University,Wuzhou 543002,China;Guangxi Colleges and Universities Key Laboratory of Professional Software Technology,Wuzhou University,Wuzhou 543002,China;Guangxi Colleges and and Universities Key Laboratory of Image Processing and Intelligent Information System,Wuzhou University,Wuzhou 543002,China;School of Mechanical and Material Engineering,Wuzhou University,Wuzhou 543002,China)

机构地区：[1]梧州学院大数据与软件工程学院,广西梧州543002 [2]梧州学院广西高校行业软件技术重点实验室,广西梧州543002 [3]梧州学院广西高校图像处理与智能信息系统重点实验室,广西梧州543002 [4]梧州学院机械与材料工程学院,广西梧州543002

出　　处：《安徽大学学报（自然科学版）》2020年第1期31-36,共6页Journal of Anhui University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(51765060);广西自然科学基金资助项目(2018JJB170034);广西高校中青年教师基础能力提升项目(2018KY0543);梧州学院校级科研重点项目(2016B008)。

摘　　要：研究一类具有非线性中立项的二阶变时滞微分方程的振动性.利用广义的Riccati变换及有关不等式,获得该类方程振动的两个新的判别定理,这些定理能用于其他已知结果不适用的情形.特别地,获得的Hille型和Kamenev型振动准则推广并改进了相关文献中的一些已知结果.We study the oscillatory behavior of a certain class of second-order variable delay differential equations with a nonlinear neutral term in this article.By using the generalized Riccati transformation and inequality technique,two new oscillation theorems are presented that can be used in cases where known results fail to apply.In particular,the Hille-type and the Kamenev-type oscillation criteria obtained extend and improve some related results reported in the literature.

关 键 词：振动性 变时滞 非线性中立项 

分 类 号：O175.7[理学—数学]