Periodic solutions of nonlinear integral equations
type: Item
instance of: scholarly article
title: Periodic solutions of nonlinear integral equations
zbMATH Open document ID: 0651.45002
DOI: 10.1007/BF01761466
author: S. H. Smith
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1988-01-01T00:00:00Z
review text: The author considers the existence of periodic solutions of the system \(x(t)=f(t)+\int^{t}_{-\infty}q(t,s,x(s))ds,\) where \(f(t+T)=f(t)\) and \(q(t+T,s+T,x)=q(t,s,x)\). Under the assumptions that the solutions are bounded in a certain sense involving weight functions and depend continuously on initial functions, the existence of a periodic solution is established with the aid of Horn's fixed point theorem. Some conditions are given that imply the assumptions on boundedness and continuous dependence.
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45M99
zbMATH DE Number: 4061879
zbMATH Keywords: periodic solutions
zbMATH Keywords: system
zbMATH Keywords: Horn's fixed point theorem
zbMATH Keywords: boundedness
zbMATH Keywords: continuous dependence
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4061879