Inverse problems: Dense nodal subset on an interior subinterval

被引:46
作者
Guo, Yongxia [1 ]
Wei, Guangsheng [1 ]
机构
[1] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian 710062, Peoples R China
关键词
Sturm-Liouville problem; Inverse nodal problem; Interior spectral data; STURM-LIOUVILLE OPERATOR;
D O I
10.1016/j.jde.2013.06.006
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The inverse nodal problem for the Sturm-Liouville problems defined on interval [0, 1] with separated boundary conditions is considered. We prove that a twin dense subset of the nodal set in interior subinterval [a(1), a(2)](subset of [0,1]) uniquely determines the potential on [0, 1] and the boundary conditions, through two cases of 1/2 is an element of [a(1), a(2)] and 1/2 is not an element of [a(1), a(2)]. Note that, for the latter, we need additional spectral information, which is associated with the derivatives of eigenfunctions at some known nodal points. (c) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码:2002 / 2017
页数:16
相关论文
共 23 条
[1]  
[Anonymous], 1991, MATH ITS APPL SOVIET
[2]   Incomplete Inverse Spectral and Nodal Problems for Differential Pencils [J].
Buterin, S. A. ;
Shieh, C-T .
RESULTS IN MATHEMATICS, 2012, 62 (1-2) :167-179
[3]   Inverse nodal problem for differential pencils [J].
Buterin, S. A. ;
Shieh, Chung Tsun .
APPLIED MATHEMATICS LETTERS, 2009, 22 (08) :1240-1247
[4]   RECONSTRUCTING POTENTIALS FROM ZEROS OF ONE EIGENFUNCTION [J].
Chen, Xinfu ;
Cheng, Y. H. ;
Law, C. K. .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2011, 363 (09) :4831-4851
[5]   L1 convergence of the reconstruction formula for the potential function [J].
Chen, YT ;
Cheng, YH ;
Law, CK ;
Tsay, J .
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 130 (08) :2319-2324
[6]   Remarks on a new inverse nodal problem [J].
Cheng, YH ;
Law, CK ;
Tsay, J .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2000, 248 (01) :145-155
[7]  
EVERITT WN, 1972, J LOND MATH SOC, V4, P443
[8]   Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum [J].
Gesztesy, F ;
Simon, B .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2000, 352 (06) :2765-2787
[9]  
Guo Y., 2013, INVERSE STURM LIOUVI
[10]   SOLUTIONS OF INVERSE NODAL PROBLEMS [J].
HALD, OH ;
MCLAUGHLIN, JR .
INVERSE PROBLEMS, 1989, 5 (03) :307-347