A generalization of three spectra theorem for inverse Sturm-Liouville Problems

In this paper we generalize the inverse three spectra theorem for Sturm-Liouville problems. When the boundary problems on [0, 1/2] and [1/2, 1] subject two different boundary conditions at the midpoint x = 1/2, we show that under suitable circumstances, the potential and boundary conditions at endpoints x = 0, 1 are uniquely determined by the spectra of three boundary problems generated by the equation on the intervals [0, 1], [0, 1/2] and [1/2, 1], respectively. (C) 2014 Elsevier Ltd. All rights reserved.