A unuqueness theorem for Sturm-Lioville operators with eigenparameter dependent boundary conditions

In this paper, we discuss the inverse problem for Sturm- Liouville operators with boundary conditions having fractional linear function of spectral parameter on the finite interval $[0, 1].$ Using Weyl m-function techniques, we establish a uniqueness theorem. i.e., If q(x) is prescribed on $[0,\frac{1}{2}+\alpha]$ for some $\alpha\in [0,1),$ then the potential $q(x)$ on the interval $[0, 1]$ and fractional linear function $\frac{a_2\lambda+b_2}{c_2\lambda+d_2}$ of the boundary condition are uniquely determined by a subset $S\subset \sigma (L)$ and fractional linear function $\frac{a_1\lambda+b_1}{c_1\lambda+d_1}$ of the boundary condition.