Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 1069-1080 |
Number of pages | 12 |
Journal | Czechoslovak Mathematical Journal |
Volume | 69 |
Issue number | 4 |
DOIs | |
State | Published - 1 Dec 2019 |
Keywords
- 34A30
- 34B05
- 34B40
- admissible pair
- delayed argument
- linear differential equation
ASJC Scopus subject areas
- General Mathematics