| 一类二阶非线性中立型差分方程的振动性（英文） |
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| 引用本文： | YANGJia shan,LIUXing yuan. 一类二阶非线性中立型差分方程的振动性（英文）[J]. 昆明理工大学学报(自然科学版), 2012, 0(5): 88-94 |
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| 作者姓名： | YANGJia shan LIUXing yuan |
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| 作者单位： | ＤｅｐａｒｔｍｅｎｔｏｆＳｃｉｅｎｃｅａｎｄＩｎｆｏｒｍａｔｉｏｎ，ＳｈａｏｙａｎｇＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｏｙａｎｇ，Ｈｕｎａｎ４２２００４，Ｃｈｉｎ |
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| 基金项目： | Supported by the Natural Science Foundation of Hunan Province（12JJ6006）; Hunan Province Science and Technology Project（2012FJ3107）; the National Natural Science Foundation of China（11071222） |
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| 摘 要： | 研究了一类具有正负系数的二阶非线性中立型变时滞差分方程的振动性,利用Banach空间的不动点原理,通过引入参数函数,结合Riccati变换和一些分析技巧,获得了该类方程存在非振动解的一些新的准则,并同时得到了该类方程振动的判别准则,所得结论推广并改进了现有文献中的一系列结果,并举例说明了定理的应用.
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| 关 键 词： | 正负系数 中立型差分方程 变时滞 振动和非振动 Riccati变换 |
OscillationofaClassofSecondOrderNonlinear NeutralDifferenceEquations |
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| YANG Jia-shan,LIU Xing-yuan. OscillationofaClassofSecondOrderNonlinear NeutralDifferenceEquations[J]. Journal of Kunming University of Science and Technology(Natural Science Edition), 2012, 0(5): 88-94 |
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| Authors: | YANG Jia-shan LIU Xing-yuan |
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| Affiliation: | (Department of Science and Information,Shaoyang University,Shaoyang,Hunan 422004,China) |
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| Abstract: | This paper discusses the oscillation of a class of second order nonlinear neutral delay difference equation with positive and negative coefficients.Using the fixed point theorem in Banach space,and by introducing parameter function and the generalized Riccati transformation and some necessary analytic techniques,some new nonoscillation criteria for the equation are obtained.In addition,a sufficient condition for the oscillation of the equation is proposed.Some existing results in the literatures are further improved and extended.Examples are presented to illustrate the effects of the theorems. |
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| Keywords: | positive and negative coefficient neutral difference equation variable delay oscillation and nonoscillation Riccati transformation |
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