An inverse three spectra problem for Sturm–Liouville operators

Abstract

Abstract In this paper, we consider the inverse three spectra problems of recovering the Sturm–Liouville equation by the spectra of the Neumann–Dirichlet boundary value problem on [0,1] $[0,1]$, the Neumann–Robin problem on [0,1/2] $[0,1/2]$, and the Robin–Dirichlet problem on [1/2,1] $[1/2,1]$, where the two Robin parameters at the interior node x=1/2 $x=1/2$ are considered to be different. The algorithm of construction is presented and sufficient conditions for three sequences to be the spectral data of the mentioned boundary problems are given.

Keywords

• Sturm–Liouville problem
• Inverse three spectra problem
• Boundary condition