محمد شهریاری

This paper deals with the boundary value problem involving the differential equation -y''+qy=\lambda y, subject to the parameter dependent boundary conditions with finite number of transmission conditions. The potential function $ q\in L^{2}(0,\pi)$ is real and $\lambda$ is a spectral parameter. We develop the Hochstadt's results based on the transformation operator for inverse Sturm--Liouville problem when there are finite number of transmission and parameter dependent boundary conditions. Furthermore, we establish a formula for $q(x)-\tilde{q}(x)$ in the finite interval $[0,\pi]$, where $q(x)$ and $\tilde{q}(x)$ are analogous functions.