Iso-bispectral potentials for Sturm–Liouville-type operators with small delay

The paper addresses nonlinear inverse Sturm–Liouville-type problems with constant delay. Since many processes in the real world possess nonlocal nature, operators delay as well other classes of are continuously finding numerous applications natural sciences and engineering. However, spite a large number works devoted to for delay, existing results do not give comprehensive picture all values parameter. Namely, small delays, even such basic question unique solvability problem has been remaining open years. approximate classical Sturm–Liouville soon parameter tends zero, researchers expected case. Here we give, however, negative answer this long-term by constructing infinite families iso-bispectral potentials. For purpose, develop unified general approach that simultaneously covers various types boundary conditions allows one significantly shorten related proofs.