| 奇型Sturm-Liouville算子的半逆问题 |
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| 引用本文： | 王於平,杨传富,黄振友.奇型Sturm-Liouville算子的半逆问题[J].大学数学,2012(1):119-123. |
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| 作者姓名： | 王於平 杨传富 黄振友 |
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| 作者单位： | 南京林业大学理学院应用数学系;南京理工大学理学院应用数学系 |
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| 基金项目： | 江苏省自然科学基金(BK2010489);国家自然科学基金(11171152) |
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| 摘 要： | 奇型Sturm-Liouville问题的势函数q(x)由两组谱唯一确定的,Sturm-Liouville算子的半逆问题讨论由一组谱和一半势函数唯一确定势函数q(x).本文利用Koyunbakan和Panakhov的方法,证明一组谱和(π/2,π)上的势函数q(x)唯一确定(0,π)上Sturm-Liouville方程含有奇型的1sin2x的势函数q(x).
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| 关 键 词： | 谱 势函数 Sturm-Liouville算子 |
Half Inverse Problem for Singular Sturm-Liouwille Operators |
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| WANG Yu-ping,YANG Chuan-fu,HUANG Zhen-you.Half Inverse Problem for Singular Sturm-Liouwille Operators[J].College Mathematics,2012(1):119-123. |
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| Authors: | WANG Yu-ping YANG Chuan-fu HUANG Zhen-you |
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| Institution: | 1.Department of Applied Mathematics,Nanjing Forestry University,Nanjing 210037,China;2.Department of Applied Mathematics,Nanjing University of Science and Technology,Nanjing 210094,China) |
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| Abstract: | The potential q(x) of singular Sturm-Liouville operators can be uniquely determined from two spectrum.Half-inverse problem for Sturm-Liouville operators consists of reconstruction of this operator by its spectrum and half of the potential.In this paper,using Koyunbakn and Panakhov’s method,we show that if q(x) is prescribed on(π/2,π),then only one spectrum is sufficient to determine q(x) on the interval(0,π) for the Sturm-Liouville equation having singularity type 1/sin2x on(0,π). |
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| Keywords: | spectrum potential Sturm-Liouville operator |
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