Half inverse problems for the impulsive operator with eigenvalue-dependent boundary conditions

Abstract

In this work we study a Sturm-Liouville operator with a piece-wise continuous coefficient and a spectral parameter in the boundary condition. We show that if the potential function is ascertained in $(\pi/2, \pi)$ then one spectrum suffices to determinate the potential function in the whole of the interval.

Keywords

• Half inverse problem
• impulsive operator
• spectral boundary condition