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

  Published:2011-04-14
 Printed: Sep 2011
  • A. Neamaty,
    Department of Mathematics, University of Mazandaran, Babolsar, IRAN
  • S. Mosazadeh,
    Department of Mathematics, University of Mazandaran, Babolsar, IRAN
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Abstract

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: turning point, singularity, Sturm-Liouville, infinite products, Hadamard's theorem, eigenvalues turning point, singularity, Sturm-Liouville, infinite products, Hadamard's theorem, eigenvalues
MSC Classifications: 34B05, 34Lxx, 47E05 show english descriptions Linear boundary value problems
Ordinary differential operators [See also 47E05]
Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)
34B05 - Linear boundary value problems
34Lxx - Ordinary differential operators [See also 47E05]
47E05 - Ordinary differential operators [See also 34Bxx, 34Lxx] (should also be assigned at least one other classification number in section 47)
 

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