Interval oscillation criteria for nonlinear differential equations with impulses and variable delay

被引：2

作者：

Zhou, Xiaoliang ^{[1
]}

Liu, Changdong ^{[2
]}

Wang, Wu-Sheng ^{[3
]}

机构：

[1] Lingnan Normal Univ, Dept Math, Zhanjiang 524048, Guangdong, Peoples R China

[2] Guangdong Ocean Univ, Dept Math, Zhanjiang 524088, Guangdong, Peoples R China

[3] Hechi Univ, Dept Math, Yizhou 546300, Guangxi, Peoples R China

来源：

APPLIED MATHEMATICS LETTERS | 2018年 / 85卷

关键词：

Interval oscillation; Impulse; Variable delay; Interval delay function; FORCED OSCILLATION;

D O I：

10.1016/j.aml.2018.06.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the interval qualitative properties of a class of second order nonlinear differential equations are studied. For the hypothesis of delay tau(t) being variable, the definitions of "strong zero point" and "weak zero point" are introduced and their effects on the estimation of function x(t - tau(t))/x(t) on each considered interval are investigated, then Riccati transformation and omega functions are applied to obtain interval oscillation criteria. The known results gained by Huang and Feng (2010) for tau(t) being constant and by Zhou and Wang (2016) for tau(t) being variable are developed. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：150 / 156

页数：7

共 15 条

[1] AN OSCILLATION CRITERION FOR A FORCED 2ND-ORDER LINEAR-DIFFERENTIAL EQUATION [J].

ELSAYED, MA .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 118 (03) :813-817

[2] Interval Oscillation Criteria of Second Order Mixed Nonlinear Impulsive Differential Equations with Delay [J].

Guo, Zhonghai ;

Zhou, Xiaoliang ;

Wang, Wu-Sheng .

ABSTRACT AND APPLIED ANALYSIS, 2012,

[3] Interval oscillation criteria for second-order forced impulsive differential equations with mixed nonlinearities [J].

Guo, Zhonghai ;

Zhou, Xiaoliang ;

Ge, Weigao .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2011, 381 (01) :187-201

[4] Forced oscillations for second order delay differential equations with impulses [J].

Huang, Mugen ;

Feng, Weizhen .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 59 (01) :18-30

[5] Interval criteria for oscillation of second-order linear ordinary differential equations [J].

Kong, Q .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 229 (01) :258-270

[6] Oscillation of a forced super-linear second order differential equation with impulses [J].

Liu, Xiuxiang ;

Xu, Zhiting .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 53 (11) :1740-1749

[7] Oscillation criteria for a forced mixed type Emden-Fowler equation with impulses [J].

Liu, Xiuxiang ;

Xu, Zhiting .

APPLIED MATHEMATICS AND COMPUTATION, 2009, 215 (01) :283-291

[8] Forced oscillation of super-half-linear impulsive differential equations [J].

Oezbekler, A. ;

Zafer, A. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2007, 54 (06) :785-792

[9] Oscillation of solutions of second order mixed nonlinear differential equations under impulsive perturbations [J].

Ozbekler, A. ;

Zafer, A. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 61 (04) :933-940

[10] Interval criteria for the forced oscillation of super-half-linear differential equations under impulse effects [J].

Ozbekler, A. ;

Zafer, A. .

MATHEMATICAL AND COMPUTER MODELLING, 2009, 50 (1-2) :59-65

← 1 2 →