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2 results

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

  • A. Neamaty, S. Mosazadeh
  • Journal:
    Canadian Mathematical Bulletin / Volume 54 / Issue 3 / 01 September 2011
    Published online by Cambridge University Press:
    20 November 2018, pp. 506-518
    Print publication:
    01 September 2011
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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.