Existence of periodic solutions
type: Item
instance of: scholarly article
title: Existence of periodic solutions
zbMATH Open document ID: 0918.34017
DOI: 10.1007/BF02355087
author: V. V. Filippov
published in: Mathematical Notes
publication date: 1999-03-23T00:00:00Z
review text: The author develops an apparatus for proving the existence of periodic solutions to differential equations \(y'(t)=Ay(t)+f(t,y(t))\) and to differential inclusions \(y'(t)\in Ay(t)+F(t,y(t))\). Here, \(A\) is a constant \(n\times n\) matrix, \(f\) is a Carathéodory function, and \(F\) is a Carathéodory multifunction. If the equation \(y'(t)=Ay(t)\) has no nonzero periodic solutions with period \(\omega>0\) and the function \(f\) is time-periodic with period \(\omega\), then the differential equation has a periodic solution with period \(\omega\). The same result holds in case of the differential inclusion.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1238054
zbMATH Keywords: periodic solutions
zbMATH Keywords: differential equations
zbMATH Keywords: differential inclusions
reviewed by: Corneliu Ursescu
MaRDI profile type: Publication
cites work: Q4012894
cites work: The topological structure of solution spaces of ordinary differential equations
cites work: ON THE THEORY OF THE CAUCHY PROBLEM FOR AN ORDINARY DIFFERENTIAL EQUATION WITH DISCONTINUOUS RIGHT-HAND SIDE
cites work: Q4860447
cites work: On the solution sets of differential inclusions
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description: scientific article; zbMATH DE number 1238054