Abstract
In this paper we are concerned with the inverse spectral problems for energy-dependent Sturm-Liouville problems (that is, differential pencils) defined on interval $[0,1]$ with two potentials known on a subinterval $ [a_{1},a_{2}]\subset [0,1]$. We prove that the potentials on the entire interval $[0,1]$ and the boundary condition at $x=1$ are uniquely determined in terms of partial knowledge of the spectrum in the situation of $a_{1}=0$ and $a_{2}\geq 1/2$. Furthermore, in the situation of $a_{1}\gt 0$ and $1/2\in [a_{1},a_{2}]$ we need additional information on the eigenfunctions at some interior point to obtain the uniqueness of the potentials on $[0,1]$ and two boundary conditions at $x=0,1$.
Citation
Yongxia Guo. Guangsheng Wei. "INVERSE PROBLEM FOR DIFFERENTIAL PENCILS WITH INCOMPLETELY SPECTRAL INFORMATION." Taiwanese J. Math. 19 (3) 927 - 942, 2015. https://doi.org/10.11650/tjm.19.2015.3944
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