数学物理学报 ›› 2012, Vol. 32 ›› Issue (6): 1171-1178.

• 论文 • 上一篇    下一篇

具有后效的逆Sturm-Liouville问题的唯一性

王玉华|魏广生   

  1. 陕西师范大学 数学与信息科学学院 西安 710062
  • 收稿日期:2011-03-30 修回日期:2012-03-09 出版日期:2012-12-25 发布日期:2012-12-25
  • 基金资助:

    国家自然科学基金(11171198)和中央高校专项基金(GK201001002)资助

The Uniqueness for Inverse Sturm-Liouville Problems with Aftereffect

Wang-Yu-Hua, WEI Guang-Sheng   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062
  • Received:2011-03-30 Revised:2012-03-09 Online:2012-12-25 Published:2012-12-25
  • Supported by:

    国家自然科学基金(11171198)和中央高校专项基金(GK201001002)资助

摘要:

考虑具有后效的Sturm-Liouville逆特征值问题, 即带有分离型自伴边界条件的一类积-微分方程. 该文证明, 当势函数及部分区间上的核函数为已知时, 整个区间上核函数能够通过部分特征值完全确定.

关键词: 特征值, 逆问题, Sturm-Liouville问题

Abstract:

The inverse eigenvalue problem of an integro-differential equation with self-adjoint boundary conditions is considered, which may be also regarded as  a perturbation of the classical potential equation. Some uniqueness results are obtained which imply that the kernel function M can completely be determined even if only partial information is given on M together with partial information on one full spectrum, when the potention function is known.

Key words: Eigenvalue, Inverse problem, Sturm-Liouville problem

中图分类号: 

  • 34A55