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邵阳学院理学与信息科学系
纸质出版:2012
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杨甲山, 孙文兵. 一类多时滞二阶中立型微分方程的振动性[J]. 中北大学学报(自然科学版), 2012,33(4):363-368.
杨甲山, 孙文兵. Oscillation for a Class of Second Order Neutral Differential Equations with Multiple Time-Delays[J]. 2012, 33(4): 363-368.
中立型泛函微分方程的振动性在理论和应用中有着重要意义.研究了一类具有正负系数的二阶非线性中立型时滞泛函微分方程的振动性
利用Banach空间的不动点原理
通过引入参数函数并结合一些分析技巧
获得了该类方程存在非振动解的新的准则
并得到了该类方程振动的判别准则
这些准则改善了对方程的条件限制
所得结论推广并改进了现有文献中的一系列结果.
The oscillation of neutral functional differential equations has important implications theoretically and practically.The oscillation of a class of second order nonlinear neutral delay functional differential equation with positive and negative coefficients was discussed.By using the fixed point theorem in Banach space
and by introducing parameter function and certain analytic techniques
some new non-oscillation criteria for the equation were obtained.Some sufficient conditions for oscillation of the equation were proposed.These criteria can improve the restriction of the conditions for the equation.Some existed results have been further improved and extended.
Agarwal R P,Bohner M,Li Wantong.Nonoscillation and oscillation:theory for functional differential equations[M].New York:Marcel Dekker,2004.
Kulenovic M R S,Hadziomerspahic S.Existence of nonoscillatory solution of second order linear neutral delay equation[J].J.Math.Anal.Appl.,1998,228:436-448.
Gai Mingjiu,Shi Bao,Zhang Decun.Oscillation criteria for second order nonlinear differential equations of neutral type[J].Appl.Math.J.Chin.Univ.(Ser B),2001,16(2):122-126.
王晓霞,仉志余.非线性二阶中立型时滞微分方程的非振动准则[J].信阳师范学院学报(自然科学版),2001,14(1):16-21.Wang Xiaoxia,Zhang Zhiyu.Nonoscillation criteria for second order nonlinear neutral delay differential equations[J].Journal of Xinyang Teachers College(Natural Science Edition),2001,14(1):16-21.(in Chinese)
李美丽,冯伟.二阶线性中立型时滞微分方程非振动解的存在性[J].山西大学学报(自然科学版),2002,25(3):195-199.Li Meili,Feng Wei.Existence of nonoscillatory solution of second order linear neutral delay equations[J].Journal of Shanxi University(Natural Science Edition),2002,25(3):195-199.(in Chinese)
仉志余,王晓霞,林诗仲,等.非线性二阶中立型时滞微分方程的振动和非振动准则[J].系统科学与数学,2006,26(3):325-334.Zhang Zhiyu,Wang Xiaoxia,Lin Shizhong,et al.Oscillation and nonoscillation criteria for second order nonlinear neutral delay differential equations[J].Journal of Systems Science and Mathematical Sciences,2006,26(3):325-334.(in Chinese)
Manojlovic J,Shoukaku Y,Tanigawa T,et al.Oscillation criteria for second order differential equations with positive and negative coefficients[J].Applied Mathematics and Computation,2006,181(2):853-863.
李秀云,刘召爽,俞元洪.具有正负系数的二阶中立型时滞微分方程的振动性[J].上海交通大学学报,2004,38(6):1028-1030.Li Xiuyun,Liu Zhaoshuang,Yu Yuanhong.Oscillation of second-order neutral delay differential equations with positive and negative coefficients[J].Journal of Shanghai Jiaotong University,2004,38(6):1028-1030.(in Chinese)
何宏庆,仉志余.二阶非线性中立型时滞微分方程的振动准则[J].数学的实践与认识,2007,37(23):130-134.He Hongqing,Zhang Zhiyu.Oscillation criteria for the second-order nonlinear neutral delay differential equations[J].Mathematics in Practice and Theory,2007,37(23):130-134.(in Chinese)
杨甲山.具有正负系数的二阶非线性中立型方程的非振动准则[J].工程数学学报,2010,27(1):118124.Yang Jiashan.Nonoscillation criteria for second order nonlinear neutral equations with positive and negative coefficients[J].Chinese Journal of Engineering Mathematics,2010,27(1):118-124.(in Chinese)
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