Incomplete inverse problems for the Sturm-Liouville type differential equation with the spectral boundary condition

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}{۲},\pi\right)  then a single spectrum suffices to determine p(x) on (۰,\pi). Moreover, applying Gesztesy-Simon's method, we demonstrate that if p(x)  is assumed over the given segment [\pi/۲(۱ - \theta), \pi] where \theta \in (۰, ۱), a finite number of the spectrum is enough to give p(x) on (۰, \pi).

کلیدواژه ها:

Sturm-Liouville equation ، Inverse problem ، Spectrum