The extrema of the first eigenvalue of the Sturm--Liouville problem with third-type boundary conditions

2017/04/30 by E. S. Karulina, Karulina, E. S.
Mathematics · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory in Mathematical Physics #math.CA

paper · pdf · doi:10.48550/arxiv.1705.00255

in Russian

arxiv created 2017/04/30 · openalex publication_date 2017/04/30 · arxiv updated 2017/05/02 · openalex created_date 2017/05/12 · openalex updated_date 2026/07/28

Abstract

We get the infima and suprema of the first eigenvalue of the problem y'' + qy + λy = 0, y'(0) - k₀² y(0) = y'(1) + k₁² y(1) = 0, where q belongs to the set of nonnegative summable functions on [0,1] such that ∫₀¹ q^γdx = 1, where γ∈ R∖ \0\.

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