时间尺度上三阶Emden-Fowler中立型时滞动力方程的振动性和渐近性  

Oscillation and Asymptotic Behavior for Third-order Emden-Fowler Neutral Delay Dynamic Equation on Time Scales

作　　者：仉志余 张燕燕 俞元洪[3] ZHANG ZHIYU;ZHANG YANYAN;YU YUANHONG(Department of Sciences,Taigyuan Institute of Techmology,Taiyuan 030008,China;School of Science,North University of China,Taiyuan 030051,China;Academy of Mathematics and Systens Science,Chinese Academy of Sciences,Beijing 100190,China)

机构地区：[1]太原工业学院理学系,太原030008 [2]中北大学理学院,太原030051 [3]中国科学院数学与系统科学研究院,北京100190

出　　处：《应用数学学报》2020年第3期502-516,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11701528,11647034);山西省自然科学基金(2011011002-3)资助项目.

摘　　要：伴随着科学技术的发展,时间尺度上动力方程的振动性研究在诸如种群动力学模型和电子工程、量子力学和航空航天科技工程中的Keller振荡模型的应用中有着越来越重要的作用.近年来,对时间尺度上二阶动力方程的研究已有许多成果,但对三阶动力方程的研究相对不够完善,因此对三阶动力方程振动性和渐进性的研究具有重要意义.本文研究一类时间尺度上三阶非线性中立型Emden-Fowler时滞动力方程的振动性和渐近性,利用Riccati变换及不等式技巧,建立了该类方程几个新的Leighton型,Kemenev型和Philos型振动准则,推广,改进和统一了已有文献中包括该类微分方程和差分方程的相关结果,并给出实例展示了本文主要结论的效果.With the development of science and technology,the study of the Oscillation of dynamic equations on time scales has important applications in biological population dynamics models,Keller oscillation models in electronic engineering,quantum dynamics,and aerospace science and engineering.In recent years,there have been many results on the study of the second-order dynamic equations on the time scales,and the results of the thirdorder dynamic equations are not perfect,so it is of great significance to study the third-order dynamic equations.In this paper,we study the oscillation and asymptotic behavior for a class of third-order Emden-Fowler neutral delay dynamic equations on time scales.Using Riccati transformation and inequality techniques,the Leighton-type,Kemenev-type and Philos-type vibration criteria for this kind of equations are established,and some conclusions obtained in this paper generalize the known results.And some concrete examples are given to illustrate the main conclusions of this paper.

关 键 词：时间尺度 三阶非线性动力方程 EMDEN-FOWLER方程 中立型 振动准则 渐近性 

分 类 号：O175[理学—数学]