ON THE CANONICAL SOLUTION AND DUAL EQUATIONS OF STURM-LIOUVILLE PROBLEM WITH SINGULARITY AND TURNING POINT

Authors

Department of Mathematics, University of Mazandaran, Babolsar, I. R. of Iran

Abstract

In this paper, we investigate the canonical property of solutions of a system of differential
equations having a singularity and turning point of even order. First, by a replacement, we transform the
system to the Sturm-Liouville equation with a turning point. Using the asymptotic estimates for a special
fundamental system of solutions of Sturm-Liouville equation, we study the infinite product representation of
solutions of the system and investigate the uniqueness of the solution for the dual equations of the Sturm-
Liouville equation. Then, we transform the Sturm-Liouville equation with a turning point to the equation with
a singularity, and study the asymptotic behavior of its solutions. Such representations are relevant to the
inverse spectral problem.

Keywords

Iranian Journal of Science
Volume 34, Issue 1 - Serial Number 1
January and February 2010
Pages 71-88

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