时间轴上二阶非线性非自治延迟动力系统的振动性  

Oscillation of Second-Order Nonlinear Nonautonomous Delay Dynamic Equations on Time Scales

作　　者：张萍 杨甲山 覃桂茳 Zhang Ping;Yang Jiashan;Qin Guijiang(School of Science,Shaoyang University,Hunan Shaoyang 422004;School of Data Science and Software Engineering,Wuzhou University,Guangxi Wuzhou 543002)

机构地区：[1]邵阳学院理学院,湖南邵阳422004 [2]梧州学院大数据与软件工程学院,广西梧州543002

出　　处：《数学物理学报（A辑）》2022年第3期839-850,共12页Acta Mathematica Scientia

基　　金：国家自然科学基金(51765060);湖南省教育厅一般项目(20C1683);广西自然科学基金(2020JJA110021);广西高校中青年教师基础能力提升项目(2020KY17007);梧州学院校级科研重点项目(2020B005);邵阳市科技计划项目(2021005ZD)~~。

摘　　要：研究了时间轴T上一类二阶非线性非自治变延迟的阻尼动态方程的振动性,考虑的是方程为非正则情形,通过引入广义Riccati变换,借助时间轴上的理论和一些经典不等式,建立了该方程振动的一些新准则,这些振动准则充分反应了延迟函数和阻尼项在系统振动中的影响作用.所举例子说明,所得准则不仅推广、改进并丰富了一些已知结果,而且具有较好的有效性和实用性.The oscillatory behavior of a class of second-order nonlinear nonautonomous variable delay damped dynamic equations are studied on a time scale T,where the equations are noncanonical form.By using the generalized Riccati transformation,and the time scales theory and the classical inequality,we establish some new oscillation criteria for the equation.The results fully reflect the influential actions of delay functions and damping terms in system oscillation.Finally,some examples are given to show that our results extend,improve and enrich those reported in the literature,and that they have good effectiveness and practicability.

关 键 词：振动性 时间轴 Emden-Fowler型动力系统 RICCATI变换 

分 类 号：O175.1[理学—数学]