Periodic perturbations of a class of functional differential equations
type: Item
instance of: scholarly article
title: Periodic perturbations of a class of functional differential equations
zbMATH Open document ID: 1500.34059
author: Marco Spadini
published in: Journal of Dynamics and Differential Equations
publication date: 2022-03-17T00:00:00Z
review text: In this paper, the author studies the existence of a connected ``branch'' of periodic solutions of \(T\)-periodic perturbations of a particular class of functional differential equations on differentiable manifolds. Their result is obtained by a combination of degree-theoretic methods and a technique that allows to associate the bounded solutions of the functional equation to bounded solutions of a suitable ordinary differential equation. The author develops their analysis using methods inspired by \textit{M. Furi} et al. [in: Handbook of topological fixed point theory. Berlin: Springer. 741--782 (2005; Zbl 1089.47046); \textit{M. Furi} and \textit{M. Spadini}, Nonlinear Anal., Theory Methods Appl. 29, No. 8, 963--970 (1997; Zbl 0885.34041)]. However, the techniques developed in those papers do not apply directly to perturbations of general functional differential equations but, for the particular form the author observes that the study of periodic solutions can be reduced to the study of the periodic solution of an ordinary differential equation on a higher dimensional manifold. The authors point out that, at the price of some more minor technicalities, the same ``reduction'' strategy adopted in this paper could be applied to the more general case when the periodic perturbation depends also on a retarded term, with delay that might be fixed or functional (possibly infinite).
reviewed by: Yingxin Guo
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 34K27
Mathematics Subject Classification ID: 34K17
Mathematics Subject Classification ID: 34C40
zbMATH DE Number: 7491618
zbMATH Keywords: functional differential equations
zbMATH Keywords: branches of periodic solutions
zbMATH Keywords: degree of tangent vector field
MaRDI profile type: Publication
full work available at URL: s10884-020-09928-2
OpenAlex ID: W3123339605
Wikidata QID: Q115383316
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DOI: 10.1007/S10884-020-09928-2
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description: scientific article; zbMATH DE number 7491618