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 (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 (Formula presented.) 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 (Formula presented.) there exists a unique solution (Formula presented.) of the above equation; (2) there is an absolute constant c(p) ∈ (0, ∞) such that regardless of the choice of a function (Formula presented.) the solution of the above equation satisfies the inequality (Formula presented.).

Original languageAmerican English
Pages (from-to)477-511
Number of pages35
JournalCzechoslovak Mathematical Journal
Volume72
Issue number2
DOIs
StatePublished - 1 Jun 2022

Keywords

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

All Science Journal Classification (ASJC) codes

  • General Mathematics

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