Asymptotics and oscillation of nth-order nonlinear dynamic equations on time scales

被引：8

作者：

Zhang, Shao-Yan ^{[1
]}

Wang, Qi-Ru ^{[2
]}

Kong, Qingkai ^{[3
]}

机构：

[1] Guangdong Univ Finance, Dept Math, Guangzhou 510520, Guangdong, Peoples R China

[2] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China

[3] No Illinois Univ, Dept Math Sci, De Kalb, IL USA

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2016年 / 275卷

关键词：

nth-order nonlinear dynamic equation; Time scales; Oscillation; Asymptotics; Generalized Riccati technique; DIFFERENTIAL-EQUATIONS; CRITERIA;

D O I：

10.1016/j.amc.2015.11.084

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with nth-order nonlinear dynamic equations on time scales of the form (r(t)Phi(gamma)(chi(Delta n-1)(t)))(Delta) + Sigma(k)(i=0)q(i)(t)Phi alpha(i)(chi(delta(i)(t))) = 0 with n >= 2. By discussing the signs of nth-order derivatives of eventually positive solutions for i _ 1, ..., n - 1, and using the generalized Riccati technique and integral averaging technique, we derive new criteria for oscillation and asymptotic behavior of the equation. Our results extend many existing results in the literature. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：324 / 334

页数：11

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