Abstract
We consider the eigenvalue problem generated by the 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 and the imaginary parts of the numbers √λ n monotonically tend to infinity as n → ∞.
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Marchenko, V.A., Operatory Shturma-Liuvillya i ikh prilozheniya (Sturm-Liouville Operators and Their Applications), Kiev: Naukova Dumka, 1977.
Makin, A.S., On a Two-Point Boundary Value Problem for the Sturm-Liouville Operator with a Nonclassical Asymptotics of the Spectrum, Differ. Uravn., 2013, vol. 49, no. 5, pp. 564–572.
Kerimov, N.B., On Necessary Conditions for the Basis Property, Differ. Uravn., 1996, vol. 32, no. 6, pp. 943–953.
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Original Russian Text © A.S. Makin, 2015, published in Differentsial’nye Uravneniya, 2015, Vol. 51, No. 3, pp. 317–322.
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Makin, A.S. Problem with nonclassical eigenvalue asymptotics. Diff Equat 51, 318–324 (2015). https://doi.org/10.1134/S0012266115030040
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DOI: https://doi.org/10.1134/S0012266115030040