Half inverse problem for the discontinuous Dirac operator with the spectral parameter boundary conditions

Abstract

In this work, we consider the Dirac operator with the spectral parameter boundary conditions and the jump condition at the point $\frac{\pi}{2}$. We investigate the spectral properties and establish a new uniqueness theorem of the half inverse problem for discontinuous impulsive Dirac operator operators by constructing the Weyl function and exploiting its relevant properties. We conclude that if the potential is known on $(0,\frac{\phi(\pi)}{2})$, where $\frac{\phi(\pi)}{2}<\frac{\pi}{2}$, then the potential on $(0,\pi)$, the partial parameters in the boundary conditions and jump conditions can be uniquely determined by only one spectrum.