The Massera-Schäffer Problem for a First Order Linear Differential Equation

Nina A. Chernyavskaya, Leonid A. Shuster

Research output: Contribution to journalArticlepeer-review

Abstract

We consider the Massera-Schäffer problem for the equation −y′(x) + q(x)y(x) = f(x), where (Formula presented.). By a solution of the problem we mean any function y, absolutely continuous and satisfying the above equation almost everywhere in R. Let positive and continuous functions μ(x) and θ(x) for x ∈ R be given. Let us introduce the spaces (Formula presented.). We obtain requirements to the functions μ θ and q under which (1) for every function f ∈ Lp(R, θ) there exists a unique solution y ∈ Lp(R, μ) of the above equation; (2) there is an absolute constant c(p) ∈ (0, ∞) such that regardless of the choice of a function f ∈ Lp(R, θ) the solution of the above equation satisfies the inequality (Formula presented.).

Original languageEnglish
JournalCzechoslovak Mathematical Journal
DOIs
StateAccepted/In press - 1 Jan 2021

Keywords

  • 34A30
  • admissible space
  • first order linear differential equation

ASJC Scopus subject areas

  • Mathematics (all)

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