TY - JOUR

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

AU - Chernyavskaya, N. A.

AU - Shuster, L. A.

PY - 2008/2

Y1 - 2008/2

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

UR - http://www.scopus.com/inward/record.url?scp=55449119513&partnerID=8YFLogxK

U2 - 10.1002/mana.200510592

DO - 10.1002/mana.200510592

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AN - SCOPUS:55449119513

SN - 0025-584X

VL - 281

SP - 160

EP - 170

JO - Mathematische Nachrichten

JF - Mathematische Nachrichten

IS - 2

ER -