Incomplete inverse problems for the Sturm-Liouville type differential equation with the spectral boundary condition

Document Type : Research Paper


1 Department of Basic Sciences, Sari Agricultural Sciences and Natural Resources University, 578 Sari, Iran

2 Department of Mathematics, Faculty of Engineering Science, Quchan University of Technology, Quchan, Iran



In this study, we examine the inverse problem for the differential equation of the Sturm-Liouville type with the spectral boundary condition in the finite interval. Using Lieberman-Hochstadt's method, we show that if $p(x)$ is prescribed on the half interval  $\left(\frac{\pi}{2},\pi\right)$  then a single spectrum suffices to determine $p(x)$ on $(0,\pi)$. Moreover, applying Gesztesy-Simon's method, we demonstrate that if $p(x)$  is assumed over the given segment $[\pi/2(1 - \theta), \pi]$ where $\theta \in (0, 1),$ a finite number of the spectrum is enough to give $p(x)$ on $(0, \pi)$.


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Articles in Press, Corrected Proof
Available Online from 09 May 2024
  • Receive Date: 10 January 2024
  • Accept Date: 12 March 2024