The Half-Inverse Transmission Problem for a Sturm-Liouville-Type Differential Equation With the Fixed Delay and Non Zero Initial Function

In this paper, we consider the boundary value problem for the Sturm-Liouville type equation with the fixed delay π/2 and a non zero initial function under transmission conditions at the delay point. We study the case when all parameters within the transmission conditions are known and the potential function is known on the interval (0,π/2). We will prove the uniqueness theorem from two spectra, first with Neumann boundary conditions and second with Cauchy boundary condition. Additionally, we will present an algorithm for the construction of the potential function over the interval (π/2,π) 2020 Mathematics Subject Classification. 34K29,34B24