Acta mathematica scientia, Series B >
AMBARZUMYAN’S THEOREM WITH EIGENPARAMETER IN THE BOUNDARY CONDITIONS
Received date: 2008-12-10
Revised date: 2010-04-02
Online published: 2011-07-20
Supported by
This work was supported by Natural Science Foundation of Jiangsu Province of China (BK 2010489) and the Outstanding Plan-Zijin Star Foundation of Nanjing University of Science and Technology (AB 41366), and NUST Research Funding (AE88787), and the National Natural Science Foundation of China (11071119).
In this paper, the classical Ambarzumyan’s theorem for the regular Sturm-Liouville problem is extended to the case in which the boundary conditions are eigenpa-rameter dependent. Specifically, we show that if the spectrum of the operator −D2+q with
eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.
YANG Chuan-Fu , YANG Xiao-Ping . AMBARZUMYAN’S THEOREM WITH EIGENPARAMETER IN THE BOUNDARY CONDITIONS[J]. Acta mathematica scientia, Series B, 2011 , 31(4) : 1561 -1568 . DOI: 10.1016/S0252-9602(11)60342-1
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