Inverse Spectral Problems for Sturm–Liouville Operators with a Constant Delay Less than Half the Length of the Interval and Robin Boundary Conditions

Abstract

The topic of this paper are non-self-adjoint second-order differential operators with a constant delay, which is less than half of the length of the interval. We consider the case when a delay is from $$\tau \in [\frac{2\pi }{5},\frac{\pi }{2})$$ , and the potential is a real-valued function which satisfy $$q\in L^{2}[0,\pi ]$$ . The inverse spectral problem of recovering the potential from the spectra of two boundary value problems with Robin boundary conditions has been studied. We have proved that the delay and the potential are uniquely determined by two spectra of boundary spectral problem, one with boundary conditions $$y'(0)-hy(0)=0$$ , $$y'(\pi )+H_{1} y(\pi )=0$$ and the other with boundary conditions $$y'(0)-hy(0)=0$$ , $$y'(\pi )+H_{2} y(\pi )=0$$ .