This article is cited in 1 paper

Real, Complex and Functional analysis

On associated solutions of the system of non-autonomous differential equations in the Lebesgue spaces

A. I. Zhuk, H. Zashchuk

Brest State Technical University, 267 Maskouskaja Street, Brest 224023, Belarus

Abstract: Herein, we investigate systems of non-autonomous differential equations with generalised coefficients using the algebra of new generalised functions. We consider a system of non-autonomous differential equations with generalised coefficients as a system of equations in differentials in the algebra of new generalised functions. The solution of such a system is a new generalised function. It is shown that the different interpretations of the solutions of the given systems can be described by a unique approach of the algebra of new generalised functions. In this paper, for the first time in the literature, we describe associated solutions of the system of non-autonomous differential equations with generalised coefficients in the Lebesgue spaces $L_{P}(T)$.

Keywords: algebra of new generalised functions; differential equations with generalised coefficients; functions of finite variation.

UDC: 519.9

Received: 09.11.2021
Revised: 11.11.2021
Accepted: 15.02.2022

Language: English

DOI: 10.33581/2520-6508-2022-1-6-13