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

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.