فهرست نشریات علمی دسترسی آزاد ایران

In this study, we examine the inverse problem for the differential equation of the Sturm-Liouville type with the spectral boundary condition in the finite interval. Using Lieberman-Hochstadt's method, we show that if $p(x)$ is prescribed on the half interval  $\left(\frac{\pi}{2},\pi\right)$  then a single spectrum suffices to determine $p(x)$ on $(0,\pi)$. Moreover, applying Gesztesy-Simon's method, we demonstrate that if $p(x)$  is assumed over the given segment $[\pi/2(1 - \theta), \pi]$ where $\theta \in (0, 1),$ a finite number of the spectrum is enough to give $p(x)$ on $(0, \pi)$.