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.

**Keywords**

**Main Subjects**

Volume 41, Issue 4

July and August 2015

Pages 1031-1043

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