| 高阶微分算子带权第二特征值的上界估计 |
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| 引用本文： | 卢亦平,钱椿林. 高阶微分算子带权第二特征值的上界估计[J]. 长春大学学报, 2010, 20(6): 4-7 |
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| 作者姓名： | 卢亦平 钱椿林 |
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| 作者单位： | 苏州市职业大学基础部,江苏苏州215104 |
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| 基金项目： | 苏州市职业大学基金资助项目(SZD06L28) |
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| 摘 要： | 考虑某类高阶微分算子的带权第二特征值上界估计的问题。利用试验函数、分部积分、Rayleigh定理和不等式等方法与技巧,得到了用高阶微分算子的第一个特征值来估计第二个特征值的不等式,其估计系数与区间的几何度量无关。其不等式在物理学和力学中应用广泛,在微分方程的理论研究中起着重要的作用。
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| 关 键 词： | 高阶微分算子 特征值 上界 估计 |
The upper bound estimation of second eigenvalue for high-order differential operators with weight |
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| LU Yi-ping,QIAN Chun-lin. The upper bound estimation of second eigenvalue for high-order differential operators with weight[J]. Journal of Changchun University, 2010, 20(6): 4-7 |
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| Authors: | LU Yi-ping QIAN Chun-lin |
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| Affiliation: | LU Yi-ping,QIAN Chun-lin(Fundamental Department,Suzhou Vocational University,Suzhou 215104,China) |
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| Abstract: | This paper considers the upper bound estimation of second eigenvalue for high-order differential operators with weight.The inequality of high-order differential operators with second eigenvalue is estimated from first eigenvalue by test function method,Rayleigh theorem and inequality estimation.The estimation coefficients do not depend on the measure of the domain.This kind of problem plays an important role in the theory of differential equations and the application in mechanics and physics. |
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| Keywords: | high-order differential operator eigenvalue upper bound estimation |
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