具连续变量的高阶非线性变时滞差分方程的正解

doi:10.3969/j.issn.1007-2985.2013.03.001

journal6 ›› 2013, Vol. 34 ›› Issue (3): 1-6.DOI: 10.3969/j.issn.1007-2985.2013.03.001

• 数学 • 下一篇

具连续变量的高阶非线性变时滞差分方程的正解

(邵阳学院理学与信息科学系,湖南邵阳 422004)

出版日期:2013-05-25 发布日期:2013-07-18

Positive Solution for Nonlinear Higher-Order Neutral Variable Delay Difference Equations with Continuous Arguments

(Department of Science and Information,Shaoyang University,Shaoyang 422004,Hunan China)

Online:2013-05-25 Published:2013-07-18
About author:Yang Jia-shan(1963-),male,was born in Chengbu County,Hunan Province,professor of Shaoyang University;research area are differential and difference equation.
Supported by:
Supported by Natural Science Foundation of Hunan Province (12JJ6006);Hunan Province Science and Technology Project (2012FJ3107)

摘要/Abstract

摘要：研究了一类具有连续变量的高阶非线性变时滞中立型差分方程，利用Banach空间的不动点原理和一些分析技巧，得到了这类方程存在最终正解的几个新的充分条件，同时给出实例验证其有效性.

关键词： 最终正解, 连续变量, 非线性, 中立型时滞差分方程, 不动点原理

Abstract: Positive solution for a class of nonlinear higher-order neutral variable delay difference equations with continuous arguments is studied.Using the fixed point theorem in Banach space and a lot of inequality techniques,some sufficient conditions for the existence of eventually positive solution for the equations are obtained.The examples are presented to illustrate the effects of our theorems.

Key words: eventually positive solution, continuous arguments, nonlinear, neutral delay difference equation, fixed point theorem

杨甲山, 刘兴元. 具连续变量的高阶非线性变时滞差分方程的正解[J]. journal6, 2013, 34(3): 1-6.

YANG Jia-Shan, LIU Xing-Yuan. Positive Solution for Nonlinear Higher-Order Neutral Variable Delay Difference Equations with Continuous Arguments[J]. journal6, 2013, 34(3): 1-6.

参考文献

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[6] WANG Pei-guang,WU Meng.Oscillation Criteria of Second Order Damped Difference Equation with Continuous Variable [J].Applied Mathematics Journal of Chinese Universities(Ser.A),2006,21(1):44-48.

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[8] YANG Jia-shan.Oscillation and Nonoscillation Criteria for a Class of the Second Order Nonlinear Difference Equations with Continuous Arguments [J].Journal of Systems Science and Mathematical Sciences,2010,30(12)：1 651-1 660.

[9] YANG Jia-shan,FANG Bin.Oscillation and Nonoscillation Criteria for Higher Order Difference Equations with Continuous Arguments [J].Journal of Anhui University:Natural Science Edition,2011,35(3)：14-18.

[10] YANG Jia-shan,LI Ji-meng.Oscillation and Nonoscillation Criteria for the Higher Order Nonlinear Difference Equation with Continuous Variable [J].Journal of Hefei University of Technology:Natural Science,2010,33(6):934-938.

[11] YANG Jia-shan,WANG Yu.Existence of Positive Solutions and Oscillation for a Class of Higher Order Nonlinear Delay Difference Equations with Continuous Arguments [J].Journal of Shaoyang University:Natural Science Edition,2012,9(1):4-8.

[12] YANG Jia-shan,LI Ji-meng.The Oscillation of a Class of Higher Order Nonlinear Variable Delay Difference Equations with Continuous Arguments [J].Journal of Minzu University of China:Natural Sciences Edition,2011,20(1):31-36.

[13] LI Guo-qin,ZHONG Xiao-zhu,LIU Na,et al.Oscillation of the Second Order Neutral Delay Difference Equations with Continuous Arguments [J].Mathematics in Practice and Theory,2012,42(17):258-262.

[14] ZHONG Wen-yong.Nonlinear Boundary Value Problem for Second Order Dynamic Equations on Time Scales [J].Journal of Jishou University:Natural Sciences Edition,2012,33(4):6-10.

[15] YANG Jia-shan.Forced Oscillation of Second-Order Nonlinear Dynamic Equation with Variable Delay on Time Scales [J].Journal of Shanxi University:Natural Sciences Edition,2011,34(4):543-547.

具连续变量的高阶非线性变时滞差分方程的正解

Positive Solution for Nonlinear Higher-Order Neutral Variable Delay Difference Equations with Continuous Arguments

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