On the Nagumo uniqueness theorem

By a convenient reparametrization of the integral curves of a nonlinear ordinary differential equation (ODE), we are able to improve the conclusions of a recent generalization of Nagumo’s uniqueness theorem. In this way, we establish a flexible uniqueness criterion for ODEs without Lipschitz-like no...

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Bibliographic Details
Published in:Nonlinear analysis 2011-12, Vol.74 (17), p.6383-6386
Main Authors: Mustafa, Octavian G., O’Regan, Donal
Format: Article
Language:English
Subjects:
Criteria
Differential equations
Exact sciences and technology
Integrals
Mathematical analysis
Mathematics
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Ordinary differential equation
Ordinary differential equations
Reparametrization
Sciences and techniques of general use
Uniqueness
Uniqueness of solution
Uniqueness theorems
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Summary:By a convenient reparametrization of the integral curves of a nonlinear ordinary differential equation (ODE), we are able to improve the conclusions of a recent generalization of Nagumo’s uniqueness theorem. In this way, we establish a flexible uniqueness criterion for ODEs without Lipschitz-like nonlinearities.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2011.06.019