Correct solvability, embedding theorems and separability for the Sturm-Liouville equation

N. A. Chernyavskaya, L. A. Shuster

Research output: Contribution to journalArticlepeer-review

Abstract

For p [1,∞), f Lp(ℝ) and 0 ≤ q L1Loc(ℝ), we show that the weighted function space S(2)p (R, q) ={ y AC(1)loc (ℝ) : ∥y" qy∥p + ∥q1/p y∥p < ∞} is embedded into L p(R) if and only if the equation -y"(x) + q(x)y(x) = f (x), x ℝ, is correctly solvable in Lp(ℝ).

Original languageEnglish
Pages (from-to)45-52
Number of pages8
JournalBollettino dell'Unione Matematica Italiana
Volume8
Issue number1
DOIs
StatePublished - 8 Aug 2015

Keywords

  • Embedding theorem
  • Sobolev space
  • Sturm-Liouville equation

ASJC Scopus subject areas

  • General Mathematics

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