Inverse Problems for Sturm-Liouville-Type Differential Equation With the Fixed Delay Under Discontinuity Conditions

Abstract

In this manuscript, we consider boundary value problems for the equation with the fixed delay and transmission conditions on $\frac{\pi}{2}$. We study the case when all parameters in transmission conditions are known. We will prove theorem of uniqueness from two spectra, first with Dirichlet-Dirichlet boundary conditions and second with Dirichlet-Neumann boundary condition. Also, we implicitly give the algorithm for determining the potential from these two spectra.