Some properties of the Sturm-Liouville operator in L_p(R)

1998/09/03 by N. A. Chernyavskaya, Chernyavskaya, N. A., L. A. Shuster +1
Mathematics · #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.CA #math.SP

paper · pdf · doi:10.48550/arxiv.math/9809012

16 pages, AMS-TeX

arxiv created 1998/09/03 · openalex publication_date 1998/09/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the boundary problem -y''(x)+q(x)y(x)=f(x), lim_|x|→∞y⁽ⁱ⁾(x)=0, i=0,1, where f(x)∈ L_p(R), p∈[1,∞], 1≤ q(x)∈ L₁^\loc(R). For this boundary problem we obtain: 1) necessary and sufficient conditions for unique solvability and a priori properties of the solution; 2) a criterion for the resolvent to be compact in L_p(R), and some a priori properties of the spectrum.

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