On the speed at which solutions of the Sturm-Liouville equation tend to zero

N. A. Chernyavskaya, L. A. Shuster

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the equation - y (x) + q (x) y (x) = f (x), x R. For a fixed p [ 1, ∞) and for a correctly solvable Eq. (1) in L p (R), we find a positive and continuous function α p (x) for x R such that we have a sharp by order equality (x) = o (α p (x)), | x | → ∞, ε y D p. Here D p = { y L p (R): y, y' A C loc (R), - y + q y L p (R) }.

Original languageEnglish
Pages (from-to)193-210
Number of pages18
JournalBolletino dell Unione Matematica Italiana
Volume7
Issue number3
DOIs
StatePublished - 21 Nov 2014

Keywords

  • Estimates of solutions
  • Sturm-Liouville equation

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