On the existence of periodic and bounded solutions for functional differential equations of pointwise type with a strongly nonlinear right-hand side
type: Item
instance of: scholarly article
title: On the existence of periodic and bounded solutions for functional differential equations of pointwise type with a strongly nonlinear right-hand side
zbMATH Open document ID: 1464.34090
DOI: 10.1134/S1995080220110062
author: N. E. Zubov
published in: Lobachevskii Journal of Mathematics
publication date: 2021-01-08T00:00:00Z
review text: There is a one-to-one corresponcence between the traveling-wave-type solutions of infinite-dimensional dynamical systems and the solutions of functional-differential equations of pointwise type. The approach proposed for the study of such equations is based on a formalism whose central element is the construction of a finitely generated group \(Q\) of homeomorphisms of the line (the group operation in such a group is the superposition of two homeomorphisms). The type of functional-differential equations considered here is rather wide. At the same time, the use of the specifics of such a class of equations related to group features makes it possible to obtain advanced results for them and also to establish obstacles that prevent such equations from inheriting remarkable properties of solutions of ordinary differential equations. The main idea is from the work of \textit{L. A. Beklaryan} [Izv. Math. 84, No. 2, 209--245 (2020; Zbl 1458.34120); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 84, No. 2, 3--42 (2020)].
reviewed by: Yingxin Guo
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 34K04
zbMATH DE Number: 7291204
zbMATH Keywords: functional-differential equations
zbMATH Keywords: soliton solutions
zbMATH Keywords: Korteweg-de Vries equation
zbMATH Keywords: polynomial potential
zbMATH Keywords: periodic solitons
MaRDI profile type: Publication
Wikidata QID: Q115247365
cites work: Theory of nonlinear lattices.
cites work: Q4939475
cites work: Infinite-dimensional non-linear ordinary differential equations and the KAM theory
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full work available at URL: s1995080220110062
OpenAlex ID: W3115138581
description: scientific article; zbMATH DE number 7291204