| 王於平,黄振友,杨传富.边界条件含有特征参数的Sturm-Liouville算子的唯一性定理[J].数学年刊A辑,2012,33(4):441~448 |
| 边界条件含有特征参数的Sturm-Liouville算子的唯一性定理 |
| A Uniqueness Theorem for Sturm-Liouville Operators with Eigenparameter in Boundary Conditions |
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| DOI： |
| 中文关键词: 唯一性定理 Sturm-Liouville问题 第n特征值 参数边界条件 |
| 英文关键词:Uniqueness theorem, Sturm-Liouville problem, n-th eigenvalue,
Eigenparameter dependent on boundary condition |
| 基金项目:国家自然科学基金(No.11171152);江苏省自然科学基金(No.BK2010489)资助的项目 |
| Author Name | Affiliation | E-mail | | WANG Yuping | Department of Applied Mathematics,College of Sciences,Nanjing Forestry University,Nanjing 210037,china | ypwang@njfu.com.cn | | HUANG Zhenyou | Department of Applied Mathematics,College of Sciences,Nanjing University of Science and Technology,Nanjing 210094,china | zyhuangh@yahoo.com | | YANG Chuanfu | Department of Applied Mathematics,College of Sciences,Nanjing University of Science and Technology,Nanjing 210094,china | chuanfuyang@tom.com |
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| 中文摘要: |
| 建立了一类Sturm-Liouville问题的唯一性定理.对于固定的n∈Z,证明了该Sturm-Liouville问题的第n个特征值λn（q,a）关于a是严格单调的.对不同系数的ak,如果能够测得第n个特征值的谱集合{λn（q,ak）}k=1+∞,则谱集合{λn（q,ak）}k=1+∞能够唯一确定[0,π]上的势函数q（x）. |
| 英文摘要: |
| This paper establishes a uniqueness theorem for a kind of Sturm-Liouville
problem. For a fixed index $n\ (n\in\bf{\mathbb Z})$, it is shown
that the $n$-th eigenvalue $\lambda_{n}(q, a)$ of the
Sturm-Liouville problem is strictly monotonous in $a$.
If the spectral set $\{\lambda_{n}(q,a_k)\}_{k=1}^{+\infty}$ can
be measured for distinct $a_k$, then the potential $q(x)$ on the
interval $[0,\pi]$ can be uniquely determined by the spectral set
$\{\lambda_{n}(q,a_k)\}_{k=1}^{+\infty}$. |
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