| 王於平,杨传富,黄振友.一类奇型Sturm-Liouville算子的逆问题[J].数学年刊A辑,2011,32(6):699~704 |
| 一类奇型Sturm-Liouville算子的逆问题 |
| Inverse Problem for a Class of Singular Sturm-Liouville Operators |
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| DOI： |
| 中文关键词: 特征值 势函数 奇型Sturm-Liouville算子 逆问题 |
| 英文关键词:Eigenvalue Potential Singular Sturm-Liouville operator Inverse problem |
| 基金项目:江苏省自然科学基金(NoBK2010489); 南京理工大学卓越计划一紫金之星(NoAB41366)资助的项目 |
| Author Name | Affiliation | E-mail | | WANG Yuping | Department of Applied Mathematics,School of Science,Nanjing Forestry University,Nanjing 210037,China. | ypwang@njfu.com.cn | | YANG Chuanfu | Department of Applied Mathematics,Nanjing University of Science and Technology,Nanjing 210094,China. | chuanfuyang@tom.com | | HUANG Zhenyou | Department of Applied Mathematics,Nanjing University of Science and Technology,Nanjing 210094,China. | zyhuangh@yahoo.com |
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| 中文摘要: |
| 研究了奇型 ~Sturm-Liouville 算子的逆问题.
对于固定的 ~$n\in\mathbb{N}$, 证明了 Sturm-Liouville
问题(1.3)--(1.5)的 第 ~$n$ 个特征值 ~$\lambda_{n}(q,H)$ 关于 ~$H$
是严格单调增加的, 及一组不同边界条件下的第 ~$n$ 个特征值的谱集合
~$\{\lambda_{n}(q,H_k)\}_{k=1}^{+\infty}$
能够唯一确定 ~$(0,\pi )$ 上的势函数 ~$q(x)$. |
| 英文摘要: |
| The authors discuss the inverse problem for
a singular Sturm-Liouville operators. For a fixed $n\in\mathbb{N}$, it is shown that the $n$-th eigenvalue
$\lambda_{n}(q,H)$ of the Sturm-Liouville problems (1.3)--(1.5) is strictly increasing
in $H$, and the potential $q(x)$ on the interval $(0,\pi)$ can be uniquely determined by the spectrum set of
$\{\lambda_{n}(q,H_k)\}_{k=1}^{+\infty}$ of the $n$-th eigenvalue for different boundary conditions. |
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