Half-inverse problem for diffusion operators on the finite interval
The following uniqueness theorem is proved: Theorem. Let \(\{\lambda_n\}\) be a spectrum of the problems \[ -y''+ [q(x)+ 2\lambda p(x)] y=\lambda^2 y,\qquad x\in [0,\pi], \] \[ y'(0)- hy(0)= 0,\quad y'(\pi,\lambda)+ Hy(\pi,\lambda)= 0, \] and \[ -y''+ [\widetilde q(x)+ 2\lambda p(x)]y= \lambda^2 y,\qquad x\in [0,\pi], \] \[ y'(0)- hy(0)= 0,\quad y'(\pi,\lambda)+ Hy(\pi,\lambda)= 0, \] where \(h\), \(H\) are finite, \(p\in W^{m+1}_2[0,\pi]\), \(q,\widetilde q\in W^m_2[0,\pi]\), \(m\geq 1\) are real-valued. If \(q(x)=\widetilde q(x)\) on \([{\pi\over 2},\pi]\), then \(q(x)=\widetilde q(x)\) almost everywhere on \([0,\pi]\).
scientific article; zbMATH DE number 5125951
scientific article