Criteria for correct solvability of a general Sturm–Liouville equation in the space L1(R)

N. Chernyavskaya, L. Shuster

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We consider the equation -(r(x)y′(x))′+q(x)y(x)=f(x),x∈Rwhere f∈ L1(R) and r>0,q≥0,1/r∈L1loc(R),q∈L1loc(R),lim|d|→∞∫x-dxdtr(t)·∫x-dxq(t)dt=∞.By a solution of (1), we mean any function y, absolutely continuous in R together with ry, which satisfies (1) almost everywhere in R. Under conditions (2) and (3), we give a criterion for correct solvability of (1) in the space L1(R).

Original languageEnglish
Pages (from-to)417-443
Number of pages27
JournalBolletino dell Unione Matematica Italiana
Volume11
Issue number4
DOIs
StatePublished - 1 Dec 2018

ASJC Scopus subject areas

  • General Mathematics

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