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

Neamaty, A. ; Mosazadeh, S.

Canadian mathematical bulletin, Tome 54 (2011) no. 3, pp. 506-518

Résumé

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.

Détail

DOI : 10.4153/CMB-2011-069-7

Mots-clés : 34B05, 34Lxx, 47E05, turning point, singularity, Sturm–Liouville, infinite products, Hadamard's theorem, eigenvalues

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