On a lower a priori estimate of minimal eigenvalue of one Sturm-Liouville problem with second-type boundary conditions

2014/12/26 by А. А. Vladimirov, A. A. Vladimirov, Vladimirov, A. A. +2
Mathematics · #34L15 #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.CA #msc:34L15

paper · pdf · doi:10.48550/arxiv.1412.7986

8 pages, in Russian

openalex publication_date 2014/12/26 · arxiv created 2015/03/19 · arxiv updated 2015/03/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

It is proved that for class A_γ=\q∈ L₁[0,1]: q≥ 0, ∫₀¹ q^γ dx=1\, where γ∈ (0,1), there exists a potential q_*∈ A_γ such that minimal eigenvalue λ₁(q_*) of boundary problem -y"+q_*y=λy, y'(0)=y'(1)=0 is equal to m_γ=inf_{q∈ Aγ}λ₁(q). The equality m_γ=1 for γ≤ 1-2π^-2 and the inequality m_γ<1 for γ>1-2π^-2 are also obtained.

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