Finiteness Result for Inverse Three Spectra Sturm-Liouville Problems

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.