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一类二阶半线性泛函微分方程的振动性 被引量：1

Oscillation Criteria for a Class Second Order Functional Differential Equation
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摘要 研究二阶半线性中立型分布时滞微分方程,利用Riccati变换,积分平均和不等式技巧,得到了一切解均为振动的若干新的振动准则,推广和改进了最近文献中的一些结果. Consider oscillation criterion of second order half-linear neutral differential equations with distributed delays.By using the generalized Riccati transformation and integral averaging,new oscillation criterion are obtained for all solutions of the equations.The obtained results generalize and improve some known results.
作者 田学全 王洪珂 俞元洪
机构地区 重庆科技学院数理学院 中国科学院数学与系统科学研究院
出处 《数学的实践与认识》 CSCD 北大核心 2014年第4期286-290,共5页 Mathematics in Practice and Theory
关键词 半线性微分方程 分布时滞 振动准则 RICCATI变换 half-linear differential equation distributed delays riccati transformation oscillation criterion
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献14

  • 1Xu R,Meng F.Some new oscillation criteria for secend order quasi-linear neutral delays differential equations[J].Appl Math Comput,2006,182:797-803.
  • 2Yang X.Oscillation criteria for a class of quasi-linear differential equation[J].Appl Math Comput,2004,152:225-229.
  • 3Dosly O.Lomtatidze A.Oscillation and noniscillation criteria for half-liner second order differential equationp].Hirshima Math J,2006,36:203-219.
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  • 5张全信,高丽,俞元洪.偶阶半线性中立型分布时滞微分方程的振动性[J].应用数学学报,2011,34(5):895-905. 被引量：14
  • 6WANG P G,WU Y H.Further results on differential inequality of a class of second Order neutral type[J].Tamkng J.Math,2004,35:43-51.
  • 7Xu Z,Xia Y.Integral Averaging Technique and Oscillation Criteria Even Order Delay differential equations[J].Math anal Appl,2004,292:238-246.
  • 8Wang P G,Teo K L,Liu Y Q.Oscillation properties for even order neutral equations with distributed deviating arguments[J].Comput Appl Math,2005,182:290-303.
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  • 10张全信,俞元洪.偶阶半线性阻尼泛函微分方程的振动性[J].应用数学学报,2010,33(4):601-610. 被引量：12

二级参考文献29

  • 1Wintner A. A Criterion of Oscillatory Stability. Quart. Appl. Math., 1949, 7:115-117.
  • 2Kamenev I V. An Integral Criterion for Oscillation of Linear Differential Equations of Scend Order. Math. Zametki, 1978, 23:249-251.
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  • 4Philos Ch G. Oscillation Theorems for Linear Differential Equations of Second Order. Arch. Math., 1989, 53:482- 492.
  • 5Wang Q R. Oscillation and Asymptotics for Second-order Half-linear Differential Equations. Appl. Math. Comput., 2001, 122:253 -266.
  • 6Agarwal R P, Grace S R, O'Regan D. Oscillation Criteria for Certain nth order Differential Equations with Deviating Arguments. J. Math. Anal. Appl., 2001, 262:601-622.
  • 7Dosly O, Lomtatidze A. Oscillation and Nonoscillation Criteria for Half-linear Second order Differential Equations. Hiroshima Math. J., 2006, 36:203-219.
  • 8Hsu H B, Yeh C C. Oscillation Theorems for Second-order Half-linear Differential Equations. Appl. Math. Lett., 1999, 9: 71-77.
  • 9Xu R, Meng F. Some New Oscillation Criteria for Second order Quasi-linear Neutral Delay Differential Equations. Appl. Math. Comput., 2006, 182:797-803.
  • 10Xu Z, Xia Y. Integral Averaging Technique and Oscillation of Certain Even order Delay Differential Equations. J. Math. Anal. Appl., 2004, 292:238-246.

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数学的实践与认识
2014年 第4期

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