一类带脉冲扰动的非线性中立型广义弹性杆方程的振动分析  

Oscillation Analysis for a Class of Nonlinear Neutral Generalized Elastic Rod Equations with Impulsive Perturbation

作　　者：罗李平 曾云辉 王艳群 LUO Liping;ZENG Yunhui;WANG Yanqun(College of Mathematics and Statistics,Hengyang Normal University,Hengyang 421002,Hunan Province,China)

机构地区：[1]衡阳师范学院数学与统计学院,湖南衡阳421002

出　　处：《吉林大学学报（理学版）》2022年第6期1280-1284,共5页Journal of Jilin University:Science Edition

基　　金：湖南省自然科学基金(批准号:2022JJ90021;2022JJ50137);湖南省教育厅科研重点项目(批准号:21A0440);衡阳师范学院科研专项项目(批准号:KYZX21001);衡阳师范学院学科专项项目(批准号:XKZX21002)。

摘　　要：利用新的处理中立项的技巧和一阶脉冲时滞微分不等式的某些结果,研究一类带脉冲和中立项的非线性广义弹性杆方程的振动性问题,建立了该类弹性杆方程在第三类边界条件下所有解振动的充分性判据.所得结果表明,脉冲扰动和时滞效应在弹性杆结构振动中具有决定性作用.By using a new technique of treating neutral term and some results of first order impulsive delay differential inequalities,we investigated the oscillation problems for a class of nonlinear generalized elastic rod equations with impulse and neutral term,and established sufficient criteria for the oscillation of all solutions of this class of elastic rod equations under the third kind of boundary conditions.The obtained results reflect the decisive function of impulsive perturbation and delay effect in the oscillation of elastic rod structures.

关 键 词：振动性 广义弹性杆方程 脉冲 中立项 非线性 

分 类 号：O175.29[理学—数学]