TY - JOUR
T1 - Admissible pair of spaces for non-correctly solvable linear differential equations
AU - Chernyavskaya, Nina A.
AU - Dorel, Lela S.
AU - Shuster, Leonid A.
N1 - Publisher Copyright:
© 2016 by De Gruyter.
PY - 2016/6/1
Y1 - 2016/6/1
N2 - We consider the differential equation [Presented Equation] Under these conditions, the above equation is not correctly solvable in Lp(ℝ) for any p ϵ [1, ∞). Let q∗(x) be the Otelbaev-type average of the function q(t), t ∞ ℝ, at the point t = x; let θ(x) be a continuous positive function for x ϵ ℝ, and [Presented Equation] We show that if there exists a constant c ϵ [1, ∞) such that the inequality c-1q∗(x) ≤ θ(x) ≤ cq∗(x) holds for all x ϵ ℝ, then under some additional conditions for q the pair of spaces {Lp,θ(ℝ); Lp(ℝ)} is admissible for the considered equation.
AB - We consider the differential equation [Presented Equation] Under these conditions, the above equation is not correctly solvable in Lp(ℝ) for any p ϵ [1, ∞). Let q∗(x) be the Otelbaev-type average of the function q(t), t ∞ ℝ, at the point t = x; let θ(x) be a continuous positive function for x ϵ ℝ, and [Presented Equation] We show that if there exists a constant c ϵ [1, ∞) such that the inequality c-1q∗(x) ≤ θ(x) ≤ cq∗(x) holds for all x ϵ ℝ, then under some additional conditions for q the pair of spaces {Lp,θ(ℝ); Lp(ℝ)} is admissible for the considered equation.
KW - Linear differential equation
KW - admissible pair
KW - non-correctly solvable differential equation
UR - http://www.scopus.com/inward/record.url?scp=84973115735&partnerID=8YFLogxK
U2 - 10.1515/jaa-2016-0001
DO - 10.1515/jaa-2016-0001
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AN - SCOPUS:84973115735
SN - 1425-6908
VL - 22
SP - 1
EP - 14
JO - Journal of Applied Analysis
JF - Journal of Applied Analysis
IS - 1
ER -