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, $τ \in (\frac{π}{2},π)$ . 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 $τ$.