Matrix linearization of functional-differential equations of point type and existence and uniqueness of periodic solutions
type: Item
instance of: scholarly article
title: Matrix linearization of functional-differential equations of point type and existence and uniqueness of periodic solutions
zbMATH Open document ID: 1414.34054
DOI: 10.1134/S0012266118100014
author: L. A. Beklaryan
author: F. A. Belousov
published in: Differential Equations
publication date: 2019-03-27T00:00:00Z
review text: The paper is a continuation and generalization of the authors' earlier joint work which is given as a reference [Differ. Equ. 51, No. 12, 1541--1555 (2015; Zbl 1336.34098); translation from Differ. Uravn. 51, No. 12, 1565--1579 (2015)]. Consider the functional differential equation of the form \[\dot{x}(t) = g(t,x(t+\tau_1),\dots,x(t+\tau_s)), \quad t\in \mathbb{R}, \tag{1}\] where the function $ g(.) $ belongs to the space $C^{(r)}(\mathbb{R}\times \mathbb{R}^{n\times s};\mathbb{R}^n )$, $r\in\mathbb{N}_0 \equiv\mathbb{N}\cup\{0\} $. \par The main differences and contribution to the previous work is that the authors consider a more general case of separation of the linearized part and rearrange the functional differential equation in the matrix representation \[\dot{x}(t)= \sum_{j=1}^s A_jx(t+\tau_j+f(t,x(t+\tau_1),\dots,x(t+\tau_s)), \quad t\in\mathbb{R}\tag{2}\] where $ A_j $ is the real $ n\times n $ matrix, $ \tau_j \in [0,2\pi )$, $j\in \{1,2,\dots,s\} $. The authors study the existence of $\omega$-periodic solutions using a complicated matrix linearization.
Mathematics Subject Classification ID: 34K13
zbMATH DE Number: 7043427
reviewed by: Haydar Akca
MaRDI profile type: Publication
cites work: Periodic solutions of functional-differential equations of point type
cites work: Q3254900
cites work: Q4090945
cites work: Q5721332
full work available at URL: s0012266118100014
OpenAlex ID: W2900475927
description: scientific article; zbMATH DE number 7043427