Sharp by order estimates of solutions of a simplest singular boundary value problem

N. A. Chernyavskaya, L. A. Shuster

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We consider a boundary value problem (Equation Presented) where f ∈ Lp(ℝ), p ∈ [1,∞] (L(ℝ) := C(ℝ)) and 0 ≤ q ∈ L1loc (ℝ). For a given p ∈ [1,∞], for a correctly solvable problem (0.1) in L p(ℝ), we obtain minimal requirements to a positive, continuous function Θ (x) for x ∈ ℝ under which, regardless of f ∈ Lp(ℝ), the solution y ∈ Lp(ℝ) of problem (0.1) satisfies the equality (Equation Presented).

Original languageEnglish
Pages (from-to)160-170
Number of pages11
JournalMathematische Nachrichten
Volume281
Issue number2
DOIs
StatePublished - 1 Feb 2008

Keywords

  • Minimal rate of decrease of solutions
  • Simplest singular boundary value problem

ASJC Scopus subject areas

  • Mathematics (all)

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