On uniqueness of solutions of differential equations

Nekvinda, Miloslav

doi:10.21136/cpm.1983.118151

Časopis Pěst. Mat.

1983

DOI: 10.21136/cpm.1983.118151

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On uniqueness of solutions of differential equations

Miloslav Nekvinda¹

Abstract: Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

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2011

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Compatible and Incompatible Nonuniqueness Conditions for the Classical Cauchy Problem

Diblı́k

Nowak

2011

Abstract and Applied Analysis

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In the first part of this paper sufficient conditions for nonuniqueness of the classical Cauchy problemx˙=f(t,x),x(t0)=x0are given. As the essential tool serves a method which estimates the “distance” between two solutions with an appropriate Lyapunov function and permits to show that under certain conditions the “distance” between two different solutions vanishes at the initial point. In the second part attention is paid to conditions that are obtained by a formal inversion of uniqueness theorems of Kamke-type but cannot guarantee nonuniqueness because they are incompatible.

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Compatible and Incompatible Nonuniqueness Conditions for the Classical Cauchy Problem

Diblı́k

Nowak

2011

Abstract and Applied Analysis

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scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

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On uniqueness of solutions of differential equations

Abstract: Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.

Cited by 1 publication

References 0 publications

Compatible and Incompatible Nonuniqueness Conditions for the Classical Cauchy Problem

Compatible and Incompatible Nonuniqueness Conditions for the Classical Cauchy Problem

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