Inverse nodal problems for the Sturm-Liouville operator with eigenparameter dependent boundary conditions
Inverse nodal problems for the Sturm-Liouville operator with eigenparameter dependent boundary conditions
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DOI：
10.7153/oam-06-04
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发表时间：
2012
影响因子：
0.5
通讯作者：
Chuan-Fu Yang
中科院分区：
文献类型：
--
作者：
Chuan-Fu Yang
逆节点问题在于从给定的特征函数零点重构这个算子。本文研究了有限区间上具有特征参数依赖边界条件的Sturm-Liouville算子的逆节点问题。证明了Sturm-Liouville方程的唯一性定理：一个密集的节点子集唯一地决定了Sturm-Liouville方程的边界条件参数和势函数；并为逆节点问题的求解提供了一个建设性的步骤。数学学科分类（2010）：47A10、47A20、47A45、47A67、47B25。
An inverse nodal problem consists in reconstructing this operator from the given zeros of their eigenfunctions. In this work, we are concerned with the inverse nodal problem of the Sturm-Liouville operator with eigenparameter dependent boundary conditions on a finite interval. We prove uniqueness theorems: a dense subset of nodal points uniquely determine the parameters of the boundary conditions and the potential function of the Sturm-Liouville equation; and provide a constructive procedure for the solution of the inverse nodal problems. Mathematics subject classification (2010): 47A10, 47A20, 47A45, 47A67, 47B25.