Half inverse problems for the impulsive singular diffusion operator

Abstract

In this paper, we consider the inverse spectral problem for the impulsive Sturm-Liouville differential pencils on $\left[ 0,\pi\right] $ with the Robin boundary conditions and the jump conditions at the point $\dfrac{\pi}% {2}$. We prove that two potentials functious on the whole interval and the parameters in the boundary and jump conditions can be determined from a set of eigenvalues for two cases: (i) The potentials is given on $\left( 0,\dfrac{\pi}{4}\left( \alpha+\beta \right) \right) .$ (ii) The potentials is given on $\left( \alpha+\beta, \dfrac{\alpha+\beta}{2} \right) $, where $01$ respectively. Finally, was given interior inverse problem for same boundary problem.