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具有分布时滞的高阶中立型双曲偏微分方程的振动准则
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国家自然科学数学天元基金项目(1026033)


Oscillation criteria for high-order neutral hyperbolic partial differential equation with continuously distributed time delay
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    摘要:

    考虑了一类具有分布时滞的高阶中立型双曲泛函偏微分方程.利用Green公式、Jensen不等式,通过特征值的方法,获得了方程解在两类边值条件下振动的新的准则,所得结果推广和改进了若干文献中已有准则.

    Abstract:

    In this article,the oscillation of certain high-order neutral hyperbolic functional partial differential equation is considered.By using Green formula,Jensen inequlity,and eigenvalue method,we obtain some new oscillatory criteria on two boundary conditions that ensure the oscillation of solutions.The results obtained extend and improve a number of existing criteria in the literature.

    参考文献
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    [2] 林诗仲,周正新,俞元洪.一类具有连续分布的偏差变元的双曲型方程的振动准则[J].数学杂志,2005,25(5):521-526 LIN Shizhong,ZHOU Zhengxin,YU Yuanhong.Oscillation criteria for a class of hyperbolic equations with continuous distributed deviating arguments[J].Journal of Mathematics,2005,25(5):521-526
    [3] 罗李平,欧阳自根.非线性时滞双曲型偏微分方程解的振动性质[J].湖南师范大学自然科学学报,2007,30(1):13-16LUO Liping,OUYANG Zigen.Oscillatory properties of solutions for nonlinear delay hyperbolic partial differential equations[J].Journal of Natural Science of Hunan Normal University,2007,30(1):13-16
    [4] 王悠悠,毛梁成,林诗仲.非线性中立型时滞偏微分方程的振动原理[J].数学的实践与认识,2007,37(21):198-202WANG Youyou,MAO Liangcheng,LIN Shizhong.Osillation theorems for nonlinear neutral delay partial differential equations[J].Mathematics in Practice and Theory,2007,37(21):198202
    [5] 段惠,林诗仲.非线性中立型时滞偏微分方程的振动性[J].数学的实践与认识,2007,37(22):197202 DUAN Hui,LIN Shizhong.Oscillation of nonlinear evenorder delay partial differential equations of neutral type[J].Mathematics in Practice and Theory,2007,37(22):197202
    [6] 李爱霞,任洪善,俞元洪.高阶非线性中立型偏泛函微分方程的振动性[J].徐州师范大学学报:自然科学版,2008,26(2):4144LI Aixia,REN Hongshan,YU Yuanhong.On the oscillation for higherorder nonlinear partial functional differential equation of neutral type[J].Journal of Xuzhou Normal University:Natural Science Edition,2008,26(2):41-44
    [7] Ladde G S,Lakshmikantham V,Zhang B G.Oscillationtheory of differential equations with deviating arguments[M].New York:Macel Dekker Inc,1987:87-98
    [8] Philos Ch G.A new criterion for the oscillatory and asymptotic behavior of delay differential equations[J].BullAcad Pol Sci Mat,1981,39:61-64
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吕银平,林诗仲,丁朝刚.具有分布时滞的高阶中立型双曲偏微分方程的振动准则[J].南京信息工程大学学报(自然科学版),2011,(3):280-284
Lü Yinping, LIN Shizhong, DING Chaogang. Oscillation criteria for high-order neutral hyperbolic partial differential equation with continuously distributed time delay[J]. Journal of Nanjing University of Information Science & Technology, 2011,(3):280-284

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  • 收稿日期:2010-04-13

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