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

✍ Scribed by N. A. Chernyavskaya; L. A. Shuster

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 156 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200510592

✦ Synopsis

Abstract

We consider a boundary value problem

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where f ∈ L~p~ (ℝ), p ∈ [1, ∞] (L∞ (ℝ) ≔ C (ℝ)) and 0 ≤ q ∈ L^loc^~1~ (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 ∈ L~p~ (ℝ), the solution y ∈ L~p~ (ℝ) of problem (0.1) satisfies the equality

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. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)