Matrix representation of a sixth order Sturm-Liouville problem and related inverse problem with finite spectrum

Document Type: Research Paper

Authors

Faculty of Basic Sciences‎, ‎Sahand University of Technology‎, ‎Tabriz‎, ‎Iran

Abstract

‎In this paper‎, ‎we find matrix representation of a class of sixth order Sturm-Liouville problem (SLP) with separated‎, ‎self-adjoint boundary conditions and we show that such SLP have finite spectrum‎. ‎Also for a given matrix eigenvalue problem $HX=\lambda VX$‎, ‎where $H$ is a block tridiagonal matrix and $V$ is a block diagonal matrix‎, ‎we find a sixth order boundary value problem of Atkinson type that is equivalent to matrix eigenvalue problem.

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History

• Receive Date: 15 January 2014
• Revise Date: 05 July 2014
• Accept Date: 05 July 2014