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2011 Compatible and Incompatible Nonuniqueness Conditions for the Classical CauchyProblem
Josef Diblík, Christine Nowak
Abstr. Appl. Anal. 2011(SI1): 1-15 (2011). DOI: 10.1155/2011/743815


In the first part of this paper sufficient conditions for nonuniqueness of the classical Cauchy problem x˙=f(t,x), x(t0)=x0 are 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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Josef Diblík. Christine Nowak. "Compatible and Incompatible Nonuniqueness Conditions for the Classical CauchyProblem." Abstr. Appl. Anal. 2011 (SI1) 1 - 15, 2011.


Published: 2011
First available in Project Euclid: 12 August 2011

zbMATH: 1222.34010
MathSciNet: MR2795075
Digital Object Identifier: 10.1155/2011/743815

Rights: Copyright © 2011 Hindawi

Vol.2011 • No. SI1 • 2011
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