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    Hormozi, Mahdi 2012. A note on a paper of Harris concerning the asymptotic approximation to the eigenvalues of -y'' + qy = λy, with boundary conditions of general form. Boundary Value Problems, Vol. 2012, Issue. 1, p. 40.

    Neamaty, A. and Haghaieghy, S. 2009. On the asymptotic of an eigenvalue problem with 2n interior singularities. Proceedings - Mathematical Sciences, Vol. 119, Issue. 5, p. 619.

    Gesztesy, Fritz and Zinchenko, Maxim 2006. On spectral theory for Schrödinger operators with strongly singular potentials. Mathematische Nachrichten, Vol. 279, Issue. 9-10, p. 1041.

    Atkinson, F. V. and Fulton, C. T. 1999. Asymptotics of the Titchmarsh—Weyl m-coefficient for non-integrable potentials. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 129, Issue. 04, p. 663.

    Harris, B.J. 1988. A note on a paper of Atkinson concerning the asymptotics of an eigenvalue problem with interior singularity. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 110, Issue. 1-2, p. 63.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 99, Issue 1-2
  • January 1984, pp. 51-70

Asymptotics of Sturm-Liouville eigenvalues for problems on a finite interval with one limit-circle singularity, I*

  • F. V. Atkinson (a1) and C. T. Fulton (a2)
  • DOI:
  • Published online: 14 November 2011

Asymptotic formulae for the positive eigenvalues of a limit-circle eigenvalue problem for –y” + qy = λy on the finite interval (0, b] are obtained for potentials q which are limit circle and non-oscillatory at x = 0, under the assumption xq(x)∈L1(0,6). Potentials of the form q(x) = C/xk, 0<fc<2, are included. In the case where k = 1, an independent check based on the limit-circle theory of Fulton and an asymptotic expansion of the confluent hypergeometric function, M(a, b; z), verifies the main result.

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Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
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