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On the Canonical Solution of the Sturm–Liouville Problem with Singularity and Turning Point of Even Order

Published online by Cambridge University Press:  20 November 2018

A. Neamaty  and
S. Mosazadeh
A. Neamaty
Affiliation:
Department of Mathematics, University of Mazandaran, Babolsar, Iran e-mail: namaty@umz.ac.irs.mosazadeh@umz.ac.ir
S. Mosazadeh
Affiliation:
Department of Mathematics, University of Mazandaran, Babolsar, Iran e-mail: namaty@umz.ac.irs.mosazadeh@umz.ac.ir
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Abstract

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In this paper, we are going to investigate the canonical property of solutions of systems 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 turning point. Using of the asymptotic estimates provided by Eberhard, Freiling, and Schneider for a special fundamental system of solutions of the Sturm–Liouville equation, we study the infinite product representation of solutions of the systems. Then we transform the Sturm–Liouville equation with turning point to the equation with singularity, then we study the asymptotic behavior of its solutions. Such representations are relevant to the inverse spectral problem.

Keywords

34B0534Lxx47E05turning pointsingularitySturm–Liouvilleinfinite productsHadamard's theoremeigenvalues
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 3 , 01 September 2011 , pp. 506 - 518
Copyright
Copyright © Canadian Mathematical Society 2011

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