The Borg’s Theorem for Singular Sturm-Liouville Problem with Non-Separated Boundary Conditions

Abstract

‎In this paper‎, ‎we consider a Sturm-Liouville equation with non-separated boundary conditions on a finite interval‎. ‎We discuss some properties of solutions of the Sturm-Liouville equation‎, ‎where the potential function has a singularity in the finite interval‎. ‎We also calculate eigenvalues and prove the uniqueness of Borg's Theorem of this boundary value problem‎.

Keywords

• non-separated boundary condition
• singularities
• eigenvalues
• inverse problems