A criterion for correct solvability of the Sturm-Liouville equation in the space Lp(R)

N. Chernyavskaya, L. Shuster

Research output: Contribution to journalArticlepeer-review

18 Scopus citations

Abstract

We consider an equation (1) - y″(x) + q(x) y(x) = f(x), x ∈ R, where f(x) ∈ Lp(R), p ∈ [1, ∞] (||f|| := C(R)), and 0 ≤ q(x) ∈ L1loc(R). By a solution of equation (1), we mean any function y(x) such that y(x), y′(x) ∈ ACloc(R), and equality (1) holds almost everywhere on R. In this paper, we obtain a criterion for the correct solvability of (1) in Lp(R), p ∈ [1, ∞].

Original languageEnglish
Pages (from-to)1043-1054
Number of pages12
JournalProceedings of the American Mathematical Society
Volume130
Issue number4
DOIs
StatePublished - 1 Jan 2002

Keywords

  • Correct solvability
  • Sturm-Liouville equation

ASJC Scopus subject areas

  • Mathematics (all)
  • Applied Mathematics

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