Differential equations without uniqueness and classical topological dynamics

George R Sell

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

In this paper we present a point of view which allows one to interpret the solutions of a non-autonomous differential equation as a classical dynamical system, without assuming uniqueness of solutions of the initial value problem. In addition we are able to construct a global flow without assuming the global existence of solutions of the given differential equations. This point of view seems appropriate in the sense that many applications of the results of classical topological dynamics to the study of the solutions of differential equations can now be performed, in a straight-forward manner, without the uniqueness assumption. We shall illustrate this claim with one important application concerning the existence of periodic or almost periodic solutions.

Original languageEnglish (US)
Pages (from-to)42-56
Number of pages15
JournalJournal of Differential Equations
Volume14
Issue number1
DOIs
StatePublished - Jan 1 1973

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Topological Dynamics
Differential equations
Uniqueness
Differential equation
Nonautonomous Differential Equations
Almost Periodic Solution
Uniqueness of Solutions
Global Existence
Straight
Initial Value Problem
Existence of Solutions
Initial value problems
Dynamical system
Dynamical systems

Cite this

Differential equations without uniqueness and classical topological dynamics. / Sell, George R.

In: Journal of Differential Equations, Vol. 14, No. 1, 01.01.1973, p. 42-56.

Research output: Contribution to journalArticle

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