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

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{p}{2},p], then one spectrum is sufficient to determine the potential q(x) on the whole interval [0,p] and coefficient function \frac{a1l+b1}{c1l+d1} of the boundary condition.