THE ASYMPTOTIC BEHAVIOR AND OSCILLATION FOR A CLASS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS  

作　　者：黄先勇 邓勋环 王其如 Xianyong HUANG;Xunhuan DENG;Qiru WANG(Department of Mathematics,Guangdong University of Education,Guangzhou,510303,China;Department of Mathematics,College of Medical Information Engineering,Guangdong Pharmaceutical University,Guangzhou,510006,China;School of Mathematics,Sun Yat-sen University,Guangzhou,510275,China)

机构地区：[1]Department of Mathematics,Guangdong University of Education,Guangzhou,510303,China [2]Department of Mathematics,College of Medical Information Engineering,Guangdong Pharmaceutical University,Guangzhou,510006,China [3]School of Mathematics,Sun Yat-sen University,Guangzhou,510275,China

出　　处：《Acta Mathematica Scientia》2024年第3期925-946,共22页数学物理学报（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China(12071491,12001113)。

摘　　要：In this paper,we consider a class of third-order nonlinear delay dynamic equations.First,we establish a Kiguradze-type lemma and some useful estimates.Second,we give a sufficient and necessary condition for the existence of eventually positive solutions having upper bounds and tending to zero.Third,we obtain new oscillation criteria by employing the Potzsche chain rule.Then,using the generalized Riccati transformation technique and averaging method,we establish the Philos-type oscillation criteria.Surprisingly,the integral value of the Philos-type oscillation criteria,which guarantees that all unbounded solutions oscillate,is greater than θ_(4)(t_(1),T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.

关 键 词：nonlinear delay dynamic equations NONOSCILLATION asymptotic behavior Philostype oscillation criteria generalized Riccati transformation 

分 类 号：O175[理学—数学]