Oscillation Criteria of the First Order Nonlinear Difference Equation with Variable Delay

杨俊仙; 王雷宏

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Oscillation Criteria of the First Order Nonlinear Difference Equation with Variable Delay

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- Oscillation Criteria of the First Order Nonlinear Difference Equation with Variable Delay
- 一阶变时滞非线性差分方程解的振动准则
- Vol. 34, Issue 2, Pages: 112-116(2013)
- 作者机构：
  
  1. 安徽农业大学理学院
  2. 安徽农业大学林学与园林学院
- 作者简介：
- 基金信息：
- DOI：
  CLC：
- Published：2013
- 稿件说明：
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杨俊仙, 王雷宏. Oscillation Criteria of the First Order Nonlinear Difference Equation with Variable Delay[J]. 2013, 34(2): 112-116.
DOI：

杨俊仙, 王雷宏. Oscillation Criteria of the First Order Nonlinear Difference Equation with Variable Delay[J]. 2013, 34(2): 112-116. DOI：

摘要

在线性差分方程和非线性常时滞差分方程的基础上

通过极限与求和的方法证明了一阶变时滞非线性差分方程的非振动解具有的一些性质;进而利用反证法

假设方程有一非振动解

结合均值不等式法

得出与条件矛盾的结果.得到了一阶变时滞非线性差分方程在不同条件下所有解的振动准则

推广和改进了线性差分方程和非线性常时滞差分方程已有的相关结果.

Abstract

On the basis of linear difference equations and nonlinear constant delay difference equations

it was proved that non-oscillatory solutions of the first order nonlinear difference equation with variable delay had some properties by using limit process and summation method.And then using the absurdity

that the equation had a non-oscillatory solution was assumed

and combining with the mean value inequality method

the contradictory result was got.Then oscillation criteria for all solutions to the first order nonlinear difference equation with variable delay were obtained in different conditions.The existing results in the linear difference equations and the nonlinear difference equations with constant delay are extended and improved.

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references

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