| 膜振动Dirichlet问题的带权特征值上界估计 |
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| 引用本文： | 张晶,田立炎,钱椿林. 膜振动Dirichlet问题的带权特征值上界估计[J]. 苏州科技学院学报(自然科学版), 2007, 24(2): 11-15 |
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| 作者姓名： | 张晶 田立炎 钱椿林 |
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| 作者单位： | 苏州市职业大学,远程教育学院,江苏,苏州,215004 |
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| 摘 要： | 考虑膜振动Dirichlet问题的带权特征值上界估计，利用试验函数、分部积分以及不等式估计等方法，建立了用前n个特征值来估计第n＋1个特征值的上界估计，其估计系数与区域度量无关。这个结果在力学和物理学中有着广泛的应用。
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| 关 键 词： | 膜振动Dirjchlet问题 特征值 特征函数 带权 上界估计 |
| 文章编号： | 1672-0687（2007）02-0011-05 |
| 修稿时间： | 2006-07-14 |
Upper Estimates of Weighted Eigenvalues for Dirichlet Problem of the Membrane Vibration |
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| ZHANG Jing,TIAN Li-yan,QIAN Chun-lin. Upper Estimates of Weighted Eigenvalues for Dirichlet Problem of the Membrane Vibration[J]. Journal of University of Science and Technology of Suzhou, 2007, 24(2): 11-15 |
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| Authors: | ZHANG Jing TIAN Li-yan QIAN Chun-lin |
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| Affiliation: | Distance Education College, Suzhou Vocational University, Suzhou 215004, China |
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| Abstract: | This paper discusses the upper estimates of weighted eigenvalues for Dirichlet problem of membrane vibration.The upper estimates are obtained by using test functions,integrals,Rayleigh theorem and inequality estimation.These estimates are established conditionally that the(n+1)th eigenvalue is dependent on the above n eigenvalues and independent from the measure of the domain in which the problem is concerned.This kind of problem is significant both in the theory of partial differential equation and in the application or potential application to mechanics and physics. |
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| Keywords: | Dirichlet problem of membranevibration eigenvalue eigenfunction weighted upper estimates |
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