TY - JOUR
T1 - Admissible spaces for a first order differential equation with delayed argument
AU - Chernyavskaya, Nina A.
AU - Dorel, Lela S.
AU - Shuster, Leonid A.
N1 - Publisher Copyright:
© 2019, Mathematical Institute, Academy of Sciences of Cz.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - We consider the equation − y′(x) + q(x) y(x− φ(x)) = f(x) , x∈ ℝ, where ϕ and q (q ⩾ 1) are positive continuous functions for all x ∈ ℝ and f ∈ C(ℝ). By a solution of the equation we mean any function y, continuously differentiable everywhere in ℝ, which satisfies the equation for all x ∈ ℝ. We show that under certain additional conditions on the functions ϕ and q, the above equation has a unique solution y, satisfying the inequality ‖y′‖C(ℝ)+‖qy‖C(ℝ)⩽c‖f‖C(ℝ), where the constant c ∈ (0, ∞) does not depend on the choice of f.
AB - We consider the equation − y′(x) + q(x) y(x− φ(x)) = f(x) , x∈ ℝ, where ϕ and q (q ⩾ 1) are positive continuous functions for all x ∈ ℝ and f ∈ C(ℝ). By a solution of the equation we mean any function y, continuously differentiable everywhere in ℝ, which satisfies the equation for all x ∈ ℝ. We show that under certain additional conditions on the functions ϕ and q, the above equation has a unique solution y, satisfying the inequality ‖y′‖C(ℝ)+‖qy‖C(ℝ)⩽c‖f‖C(ℝ), where the constant c ∈ (0, ∞) does not depend on the choice of f.
KW - 34A30
KW - 34B05
KW - 34B40
KW - admissible pair
KW - delayed argument
KW - linear differential equation
UR - http://www.scopus.com/inward/record.url?scp=85066976393&partnerID=8YFLogxK
U2 - 10.21136/CMJ.2019.0062-18
DO - 10.21136/CMJ.2019.0062-18
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AN - SCOPUS:85066976393
SN - 0011-4642
VL - 69
SP - 1069
EP - 1080
JO - Czechoslovak Mathematical Journal
JF - Czechoslovak Mathematical Journal
IS - 4
ER -