The Sturm--Liouville problem with singular potential and the extrema of the first eigenvalue

2012/06/22 by E. S. Karulina, Karulina, E. S., А. А. Vladimirov +2
Mathematics · #34L15 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics #advanced mathematical theories #math.CA #msc:34L15

paper · pdf · doi:10.48550/arxiv.1206.5081

12 pages

openalex publication_date 2012/06/22 · arxiv created 2013/05/05 · arxiv updated 2013/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

On the basis of the theory of Sturm--Liouville problem with distribution coefficients we get the infima and suprema of the first eigenvalue of the problem -y" + (q-λ) y=0, y'(0) -k₀² y(0) = y'(1) + k₁² y(1) = 0, where q belongs to the set of constant-sign summable functions on [0,1] such that ∫₀¹ q dx=± 1.

Related

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• Uniform asyptotic formulae for eigenfunctions of Sturm--Liouville operators with singular potentials
• Eigenvalues of Sturm-Liouville Operators with Distributional Potentials