Oscillation and nonoscillation for second order neutral dynamic equations with positive and negative coefficients on time scales

被引：12

作者：

Deng, Xun-Huan ^{[1
]}

Wang, Qi-Ru ^{[1
]}

Agarwal, Ravi P. ^{[2
,3
]}

机构：

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

[2] Texas A&M Univ, Dept Math, Kingsville, TX 78363 USA

[3] King Abdulaziz Univ, Dept Math, Jeddah 21589, Saudi Arabia

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2014年

关键词：

neutral dynamic equations; positive and negative coefficients; oscillation and nonoscillation; lower and upper solutions; Kranoselskii's fixed point theorem;

D O I：

10.1186/1687-1847-2014-115

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate oscillation and nonoscillation of certain second order neutral dynamic equations with positive and negative coefficients. We apply the results from the theory of lower and upper solutions for related dynamic equations along with some additional estimates on positive solutions and use different techniques to obtain some oscillatory theorems. Also, we apply Kranoselskii's fixed point theorem to obtain nonoscillatory results and then give two sufficient and necessary conditions for the equations to be oscillatory. Some interesting examples are given to illustrate the versatility of our results.

引用

页数：22

共 18 条

[1] Dynamic equations on time scales: a survey [J].

Agarwal, R ;

Bohner, M ;

O'Regan, D ;

Peterson, A .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2002, 141 (1-2) :1-26

[2]

Agarwal R. P., 2003, Series in Mathematical Analysis and Applications, V5

[3]

Agarwal R. P., 2003, J DIFFER EQU APPL, V1, P1

[4] New Oscillation Criteria for Second-Order Neutral Delay Differential Equations with Positive and Negative Coefficients [J].

Bai, Yuzhen ;

Liu, Lihua .

ABSTRACT AND APPLIED ANALYSIS, 2010,

[5]

Bohner M., 2001, Dynamic Equations on Time Scales: An Introduction with Applications, DOI DOI 10.1007/978-1-4612-0201-1

[6]

Bohner M., 2003, Advances in Dynamic Equations on Time Scales, DOI DOI 10.1007/978-0-8176-8230-9

[7]

Deng XH, 2013, ELECTRON J DIFFER EQ

[8] New oscillation criteria for second order linear difference equations with positive and negative coefficients [J].

El-Morshedy, Hassan A. .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (10) :1988-1997

[9] Oscillation of second-order strongly superlinear and strongly sublinear dynamic equations [J].

Grace, Said R. ;

Agarwal, Ravi P. ;

Bohner, Martin ;

O'Regan, Donal .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (08) :3463-3471

[10]

Higgins R, 2010, ADV DYN SYST APPL, V5, P87

← 1 2 →