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数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1708-1717.

Schr\"{o}dinger 算子二次微分束的半逆问题

王於平¹|杨传富²|黄振友²

1.南京林业大学应用数学系 |南京 210037; |
2.南京理工大学应用数学系 |南京 210094

收稿日期:2010-06-21 修回日期:2011-07-24 出版日期:2011-12-25 发布日期:2011-12-25
基金资助:
南京理工大学教学改革项目(AB42640)、南京理工大学基金项目(AB41366, AE88787)和江苏省自然科学基金 (BK 2010489)资助

Half Inverse Problem for a Quadratic Pencil of |Schr\"{o}dinger Operators

WANG Wu-Ping¹, YANG Chuan-Fu², HUANG Zhen-You²

1.Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037|
2.Department of Applied Mathematics, Nanjing University of Science and Technology, Nanjing 210094

Received:2010-06-21 Revised:2011-07-24 Online:2011-12-25 Published:2011-12-25
Supported by:
南京理工大学教学改革项目(AB42640)、南京理工大学基金项目(AB41366, AE88787)和江苏省自然科学基金 (BK 2010489)资助

摘要/Abstract

摘要：

该文讨论了有限区间[0, π] 上的 Schr\"{o}dinger 算子二次微分束的半逆问题. 改进了Koyunbakan 和 Panakhov 的证明方法^[12], 证明了如果势函数(q(x), p(x)) 为[π/2, π]上的已知函数, 则一组谱能够惟一确定有限区间[0, π] 上的势函数(q(x), p(x)) 和边界条件中的系数h.

关键词: Schr\"{o}dinger 算子的二次微分束, 边值问题, 谱, 半逆问题

Abstract:

In this paper, the authors discuss the half inverse problem for a quadratic pencil of the Schr\"{o}dinger operator on the finite interval [0, π]. Improving the Koyunbakan and Panakhov's method^[12], it is showed that if the potentials (q(x), p(x)) are prescribed on [π/2, π ], then only one spectrum is sufficient to determine the potentials (q(x), p(x)) on the interval [0, π/2) for the quadratic pencil of the Schr\"{o}dinger operator on the finite interval [0, π] and coefficient h of the boundary condition.

Key words: Quadratic pencil of the Schr\"{o}dinger operator, Boundary-value problem, Spectrum, Half inverse problem

中图分类号:

34A55

王於平, 杨传富, 黄振友. Schr\"{o}dinger 算子二次微分束的半逆问题[J]. 数学物理学报, 2011, 31(6): 1708-1717.

WANG Wu-Ping, YANG Chuan-Fu, HUANG Zhen-You. Half Inverse Problem for a Quadratic Pencil of |Schr\"{o}dinger Operators[J]. Acta mathematica scientia,Series A, 2011, 31(6): 1708-1717.

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Schr\"{o}dinger 算子二次微分束的半逆问题

Half Inverse Problem for a Quadratic Pencil of |Schr\"{o}dinger Operators

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