Sharp by order estimates of solutions of a simplest singular boundary value problem |
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| Authors: | N A Chernyavskaya L A Shuster |
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| Institution: | 1. Department of Mathematics and Computer Science, Ben‐Gurion University of the Negev, P.O.B. 653, Beer‐Sheva, 84105, Israel;2. Phone: +972 8 6477810, Fax: +972 8 6477648;3. Department of Mathematics, Bar‐Ilan University, Ramat‐Gan 52900, Israel |
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| Abstract: | We consider a boundary value problem  ((0.1)) where f ∈ Lp (?), p ∈ 1, ∞] (L∞ (?) ? C (?)) and 0 ≤ q ∈ Lloc1 (?). For a given p ∈ 1, ∞], for a correctly solvable problem (0.1) in Lp (?), we obtain minimal requirements to a positive, continuous function Θ(x) for x ∈ ? under which, regardless of f ∈ Lp (?), the solution y ∈ Lp (?) of problem (0.1) satisfies the equality  . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
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| Keywords: | Simplest singular boundary value problem minimal rate of decrease of solutions |
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