时间尺度上二阶Emden-Fowler型延迟动态方程的振动性  

Oscillation for a class of second-order Emden-Fowler-type delay dynamic equations on time scales

作　　者：杨甲山 YANG Jiashan(School of Big Data and Software Engineering,Wuzhou University,Wuzhou 543002,China;Laboratory of Complex Systems Simulation and Intelligent Computing,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]梧州学院复杂系统仿真与智能计算实验室,广西梧州543002

出　　处：《振动与冲击》2018年第16期154-161,共8页Journal of Vibration and Shock

基　　金：广西教育厅科研项目(2013YB223);硕士学位授予单位立项建设项目(桂学位[2013]4号);梧州学院2014年校级科研重大项目(2014A003);国家自然科学基金(51765060)

摘　　要：研究了时间尺度上一类二阶非线性中立型阻尼Emden-Fowler型延迟泛函动态方程的振动性,利用时间尺度上的微积分理论和广义的Riccati变换、Yang不等式、H9lder不等式以及一些分析技巧,在两种情形下建立了该方程的几个新的振动准则,所得结果充分反映了阻尼项和中立项在系统振动中的影响作用,所举例子说明,这些准则不仅推广并改进了一些已有的结果,而且具有较好的实用性和可操作性.We studied the oscillatory behavior of a certain class of second-order nonlinear neutral damped Emden-Fowler-type delay functional dynamic equations on time scales.By using the calculus theory on time scales and the generalized Riccati transformation,Yang’s inequality,H lder’s inequality and mathematical analytic methods,we established some new oscillation criteria for the equations in two cases.The results fully reflect the influential actions of damping terms and neutral terms in system oscillation.The illustrative examples show that our results extend and improve those reported in the literature and that they have practicability and maneuverability.

关 键 词：振动性 Emden-Fowler型动态方程 时间尺度 阻尼项 延迟项 

分 类 号：O175.7[理学—数学]