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

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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Bibliographic Details
Published inDifferential equations Vol. 49; no. 5; pp. 536 - 544
Main Author Makin, A. S.
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.05.2013
Springer Nature B.V
Subjects
Asymptotic properties
Boundary conditions
Boundary value problems
Difference and Functional Equations
Differential equations
Eigenvalues
Infinity
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Ordinary Differential Equations
Partial Differential Equations
Spectra
Studies
Root Function
Liouville Equation
Spectral Problem
Entire Function
Exponential Type
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Summary: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 → ∞.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:0012-2661
1608-3083
DOI:10.1134/S0012266113050029