Half inverse problem for Sturm-Liouville operators with boundary conditions dependent on the spectral parameter

Abstract

In this paper, we discuss the half inverse problem for the Sturm-Liouville operator with boundary conditions dependent on the spectral parameter and show that if q(x) is prescribed on [\frac{\pi}{2},\pi], then one spectrum is sufficient to determine the potential q(x) on the whole interval [0,\pi] and coefficient function \frac{a_1\lambda+b_1}{c_1\lambda+d_1} of the boundary condition.