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Asymptotics of the spectrum of the Sturm-Liouville operator with regular boundary conditions

Abstract

On the interval (0, π), we consider the spectral problem generated by the Sturm-Liouville operator with regular but not strongly regular boundary conditions. For an arbitrary potential q(x) ∈ L 1 (0, π) [q(x) ∈ L 2(0, π)], we establish exact asymptotic formulas for the eigenvalues of this problem.

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Correspondence to A. S. Makin.

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Dedicated to Vladimir Aleksandrovich Il’in, Academician of the Russian Academy of Sciences, my teacher, in honor of his jubilee

Original Russian Text © A.S. Makin, 2008, published in Differentsial’nye Uravneniya, 2008, Vol. 44, No. 5, pp. 626–639.

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Makin, A.S. Asymptotics of the spectrum of the Sturm-Liouville operator with regular boundary conditions. Diff Equat 44, 645–658 (2008). https://doi.org/10.1134/S0012266108050066

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Keywords

  • Differential Equation
  • Asymptotic Formula
  • Spectral Problem
  • LIOUVILLE Operator
  • Obvious Relation