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 -