A new inverse problem for the diffusion operator (Q2371097)

The inverse nodal problem is studied for the boundary value problem \[ y''+(\lambda^2+\lambda p(x)+q(x))y=0,\quad x\in (0,\pi), \] \[ y'(0)-hy(0)=y'(\pi)+Hy(\pi)=0. \] It is proved that the specification of any dense set of nodal points uniquely determines \(q(x)-\int_0^1 q(t)\,dt\) provided that \(p(x)\) is known a priori.