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On a two-point boundary value problem for the Sturm-Liouville operator with a nonclassical asymptotics of the spectrum

  • Ordinary Differential Equations
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Abstract

We consider a spectral problem generated by a Sturm-Liouville equation on the interval (0, π) with degenerate boundary conditions. We prove the existence of potentials q(x) ∈ L 2(0, π) such that the multiplicities of the eigenvalues λ n monotonically tend to infinity as n → ∞.

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Authors and Affiliations

  1. Moscow State University of Instrumental Engineering and Computer Science, Moscow, Russia

    A. S. Makin

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  1. A. S. Makin
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Dedicated to Vladimir Aleksandrovich Il’in, my dear Teacher, Academician of the Russian Academy of Sciences, on the occasion of his jubilee

Original Russian Text © A.S. Makin, 2013, published in Differentsial’nye Uravneniya, 2013, Vol. 49, No. 5, pp. 564–572.

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Makin, A.S. On a two-point boundary value problem for the Sturm-Liouville operator with a nonclassical asymptotics of the spectrum. Diff Equat 49, 536–544 (2013). https://doi.org/10.1134/S0012266113050029

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  • DOI: https://doi.org/10.1134/S0012266113050029

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