A criterion for correct solvability in Lp(ℝ) of a general Sturm-Liouville equation

N. Chernyavskaya, L. Shuster

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We consider an equation-(r(x)y′(x))′+q(x)y(x)=f(x),x ∞ℝ, where f ∈ Lp(ℝ) for p ∈ (1, ∞) with the following conditions: r>0,q≥0,1/r ∈ L1 loc(ℝ) q ∈ L1loc(ℝ),∫ -∈0dt/r(t)= ∫0 dt/r(t)= ∞By a solution of the above-mentioned equations, we mean any function y that is absolutely continuous together with ry′ and satisfies it almost everywhere on . Under the above-mentioned conditions, we give a criterion for the correct solvability of the above-mentioned equation in L p(R) for p ∈ (1, ∞).

Original languageEnglish
Pages (from-to)99-120
Number of pages22
JournalJournal of the London Mathematical Society
Volume80
Issue number1
DOIs
StatePublished - 1 Jan 2009

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