Admissible spaces for a first order differential equation with delayed argument

Nina A. Chernyavskaya, Lela S. Dorel, Leonid A. Shuster

Research output: Contribution to journalArticlepeer-review


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 languageEnglish
Pages (from-to)1069-1080
Number of pages12
JournalCzechoslovak Mathematical Journal
Issue number4
StatePublished - 1 Dec 2019


  • 34A30
  • 34B05
  • 34B40
  • admissible pair
  • delayed argument
  • linear differential equation

ASJC Scopus subject areas

  • General Mathematics


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