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

N. A. Chernyavskaya; L. A. Shuster

doi:10.1002/mana.200510592

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

N. A. Chernyavskaya
, L. A. Shuster

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We consider a boundary value problem (Equation Presented) where f ∈ L_p(ℝ), p ∈ [1,∞] (L_∞(ℝ) := C(ℝ)) and 0 ≤ q ∈ L₁^loc (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 (Equation Presented).

Original language	English
Pages (from-to)	160-170
Number of pages	11
Journal	Mathematische Nachrichten
Volume	281
Issue number	2
DOIs	https://doi.org/10.1002/mana.200510592
State	Published - 1 Feb 2008

Keywords

Minimal rate of decrease of solutions
Simplest singular boundary value problem

ASJC Scopus subject areas

General Mathematics

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10.1002/mana.200510592

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title = "Sharp by order estimates of solutions of a simplest singular boundary value problem",

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).",

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T1 - Sharp by order estimates of solutions of a simplest singular boundary value problem

AU - Chernyavskaya, N. A.

AU - Shuster, L. A.

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N2 - 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).

AB - 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).

KW - Minimal rate of decrease of solutions

KW - Simplest singular boundary value problem

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DO - 10.1002/mana.200510592

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SN - 0025-584X

VL - 281

SP - 160

EP - 170

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 2

ER -

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

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