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AMJCUB
Applied Mathematics-A Journal of Chinese Universities  2020, Vol. 35 Issue (2): 193-202    DOI: 10.1007/s11766-020-3806-y
    
Inverse nodal problem for the Sturm-Liouville operator with a weight
ZHANG Ran, Murat Sat, YANG Chuan-fu
1Department of Applied Mathematics, School of Science, Nanjing University of Science and Technology,Nanjing 210094, China.
2Department of Mathematics, Faculty of Art and Sciences, Erzincan University, Erzincan, Turkey.
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Abstract   In this work, we consider the inverse nodal problem for the Sturm-Liouville problem
with a weight and the jump condition at the middle point. It is shown that the dense nodes of the
eigenfunctions can uniquely determine the potential on the whole interval and some parameters.

Key words： inverse nodal problem      Sturm-Liouville operator      discontinuous conditions      weight function     
Published: 06 July 2020
CLC:  34A55  
  34B24  
  47E05  
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ZHANG Ran
Murat Sat
YANG Chuan-fu
Cite this article:

ZHANG Ran, Murat Sat, YANG Chuan-fu. Inverse nodal problem for the Sturm-Liouville operator with a weight. Applied Mathematics-A Journal of Chinese Universities, 2020, 35(2): 193-202.

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http://www.zjujournals.com/amjcub/10.1007/s11766-020-3806-y     OR     http://www.zjujournals.com/amjcub/Y2020/V35/I2/193


Inverse nodal problem for the Sturm-Liouville operator with a weight

 In this work, we consider the inverse nodal problem for the Sturm-Liouville problem
with a weight and the jump condition at the middle point. It is shown that the dense nodes of the
eigenfunctions can uniquely determine the potential on the whole interval and some parameters.


关键词： inverse nodal problem,  Sturm-Liouville operator,  discontinuous conditions,  weight function 
[1] XU Xiao-chuan , YANG Chuan-fu. Reconstruction of the Sturm-Liouville operator with discontinuities from a particular set of eigenvalues[J]. Applied Mathematics-A Journal of Chinese Universities, 2018, 33(2): 225-.