The Kamenev type oscillation criteria of nonlinear differential equations under impulse effects

被引：0

作者：

Zhou, Xiaoliang ^{[1
]}

Wang, Wu-Sheng ^{[2
]}

机构：

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

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

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2016年

关键词：

interval oscillation; Riccati transformation; impulse; damping; INTERVAL OSCILLATION; GENERAL-CLASS; THEOREMS; ODE;

D O I：

10.1186/s13662-016-0911-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, a general class of second-order nonlinear damped differential equations under impulse effects is studied. By introducing an auxiliary function of two variables and using Riccati transformation, several Kamenev type interval oscillation criteria are established, which generalize and extend some known ones, such as those of Huang and Feng. Moreover, examples are given to illustrate the effectiveness and non-emptiness of our results.

引用

页数：14

共 24 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 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

[3] Oscillation of second-order nonlinear ODE with damping [J].

Huang, Yan ;

Meng, Fanwei .

APPLIED MATHEMATICS AND COMPUTATION, 2008, 199 (02) :644-652

[4] Oscillation criteria for forced second-order nonlinear differential equations with damping [J].

Huang, Yan ;

Meng, Fanwei .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 224 (01) :339-345

[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] Interval oscillation criteria for second-order quasi-linear nonhomogeneous differential equations with damping [J].

Li, WT .

APPLIED MATHEMATICS AND COMPUTATION, 2004, 147 (03) :753-763

[7] Interval oscillation of a general class of second-order nonlinear impulsive differential equations with nonlinear damping [J].

Li, Xiaopei ;

Zhou, Xiaoliang ;

Wang, Wu-Sheng .

APPLIED MATHEMATICS AND COMPUTATION, 2013, 219 (16) :8803-8810

[8] 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

[9] 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

[10] Sufficient conditions for the oscillation of forced super-linear second order differential equations with oscillatory potential [J].

Nasr, AH .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1998, 126 (01) :123-125

← 1 2 3 →