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 ‖y″‖C(R)+‖y′‖C(R)+‖qy‖C(R)≤c‖f‖C(R) where the constant c∈(0,∞) does not depend on the choice of f∈C(R).
|Number of pages||21|
|Journal||Journal of Differential Equations|
|State||Published - 15 Sep 2016|
- Delayed argument
- Sturm–Liouville equation
ASJC Scopus subject areas
- Applied Mathematics