A Finiteness Result for Inverse Three Spectra Sturm-Liouville Problems

Abstract

The finiteness for an inverse three spectra Sturm-Liouville problem with potential $q$ on the interval $[0,1]$ and boundary parameters $h_{0}$, $h_{1}$ is studied in this paper. Under condition that two boundary conditions at a fixed internal rational point $a$ of $(0,1)$ are different and known a priori, we show that there exist at most a finite number of triplets $(q;h_{0},h_{1})$ corresponding to the three spectra of a Sturm-Liouville equation defined on $[0,1]$, $[0,a]$ and $[a,1]$, respectively, with the same boundary conditions at two endpoints $0$ and $1$.