| 逆Sturm-Liouville问题的求解和解的唯一性问题 |
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| 引用本文： | 王喆.逆Sturm-Liouville问题的求解和解的唯一性问题[J].复旦学报(自然科学版),2004,43(3):361-365. |
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| 作者姓名： | 王喆 |
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| 作者单位： | 复旦大学,数学研究所,上海,200433 |
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| 摘 要： | 通过调整核函数K(x，t)满足的边界条件讨论一般边界条件下逆Sturm-Liouville问题的求解．同时对包括势函数q(x)对称在内的多种情况证明了逆Sturm-Liouville问题解的唯一性．最后讨论已知势函数q(x) q(1-x)所对应的一列谱如何求解逆Sturm-Liouville问题．
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| 关 键 词： | 逆问题 Sturm-Liouville问题 谱 |
| 文章编号： | 0427-7104(2004)03-0361-05 |
The Uniqueness and the Solution of the InverseSturm-Liouville Problem |
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| WANG Zhe.The Uniqueness and the Solution of the InverseSturm-Liouville Problem[J].Journal of Fudan University(Natural Science),2004,43(3):361-365. |
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| Authors: | WANG Zhe |
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| Abstract: | The problem of determining the coefficients q(x) of the Sturm-Liouville problem under the various boundary conditions using adjusting kernel function is dicussed.The uniqueness of the inverse problem in the case of symmetric potential functions is obtained.Finally the inverse problem of unique determination of the potential function in the situation when one sequence of eigenvalues is given and the potential function is of the form q(x)+q(1-x) is investigated. |
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| Keywords: | inverse problem Sturm-Liouville problem spectrum |
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