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ON THE CANONICAL SOLUTION AND DUAL EQUATIONS OF STURM-LIOUVILLE PROBLEM WITH SINGULARITY AND TURNING POINT | ||
| Iranian Journal of Science | ||
| مقاله 8، دوره 34، شماره 1، اردیبهشت 2010، صفحه 71-88 اصل مقاله (130.6 K) | ||
| شناسه دیجیتال (DOI): 10.22099/ijsts.2010.2167 | ||
| نویسندگان | ||
| A. NEAMATY* ؛ MOSAZADEH S. | ||
| Department of Mathematics, University of Mazandaran, Babolsar, I. R. of Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Turning point؛ singularity؛ sturm-liouville؛ infinite products؛ hadamard's theorem؛ dual equations؛ eigenvalues | ||
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