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

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

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In this paper,we consider a class of third-order nonlinear delay dynamic equa-tions.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 Pötzsche 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 θ4(t1,T).The results of Theorem 3.5 and Remark 3.6 are novel.Finally,we offer four examples to illustrate our results.

nonlinear delay dynamic equationsnonoscillationasymptotic behaviorPhilos-type oscillation criteriageneralized Riccati transformation

黄先勇、邓勋环、王其如

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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

National Natural Science Foundation of ChinaNational Natural Science Foundation of China

1207149112001113

2024

10.1007/s10473-024-0309-6

数学物理学报(英文版)
中科院武汉物理与数学研究所

数学物理学报(英文版)

CSTPCD
影响因子：0.256
ISSN：0252-9602
年,卷(期)：2024.44(3)