An Inverse Problems for Sturm-Liouville-Type Differential Equation With a Constant Delay - Vladičić, Vladimir; Pikula, Milenko (Sarajevo Journal of Mathematics, 2024)
The topic of this paper is non-self-adjoint second order differential operators with constant delay generated by -y''+q(x)y(x-τ) where potential q is complex-valued function, τ (π2,π) . We establish properties of the spectral characteristics and research the inverse problem of recovering operators from their spectra when y(0)=y(π)=0. We prove that the delay and the potential is uniquely determined from two spectrum, firstly when y(0)=y'(π)=0 and secondly when y(0)=y'(π)=0, of those operators. Also we will construct q and τ.