Correct solvability of the Sturm–Liouville equation with delayed argument

N. A. Chernyavskaya, L. A. Shuster

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We consider the equation −y(x)+q(x)y(x−φ(x))=f(x),x∈R where f∈C(R) and 0≤φ∈Cloc(R),1≤q∈Cloc(R). Here Cloc(R) is the set of functions continuous in every point of the number axis. By a solution of (1), we mean any function y, doubly continuously differentiable everywhere in R, which satisfies (1). We show that under certain additional conditions on the functions φ and q to (2), (1) has a unique solution y, satisfying the inequality ‖yC(R)+‖yC(R)+‖qy‖C(R)≤c‖f‖C(R) where the constant c∈(0,∞) does not depend on the choice of f∈C(R).

Original languageEnglish
Pages (from-to)3247-3267
Number of pages21
JournalJournal of Differential Equations
Issue number6
StatePublished - 15 Sep 2016


  • Delayed argument
  • Sturm–Liouville equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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