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DIBLÍK, J. NOWAK, C.
Originální název
Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem
Typ
článek v časopise - ostatní, Jost
Jazyk
angličtina
Originální abstrakt
In the first part of this paper sufficient conditions for nonuniqueness of the classical Cauchy problem $\dot{x}=f(t,x)$, $x(t_0)=x_0$ 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.
Klíčová slova
Fundamental theory of ordinary differential equations, nonuniqueness of solutions, incompatible set of conditions
Autoři
DIBLÍK, J.; NOWAK, C.
Rok RIV
2011
Vydáno
2. 8. 2011
ISSN
1085-3375
Periodikum
Abstract and Applied Analysis
Ročník
Číslo
1
Stát
Spojené státy americké
Strany od
Strany do
15
Strany počet
BibTex
@article{BUT72872, author="Josef {Diblík} and Christine {Nowak}", title="Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem", journal="Abstract and Applied Analysis", year="2011", volume="2011", number="1", pages="1--15", issn="1085-3375" }