Detail publikačního výsledku

Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem

DIBLÍK, J.; NOWAK, C.

Originální název

Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem

Anglický název

Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem

Druh

Článek recenzovaný mimo WoS a Scopus

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.

Anglický 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

Klíčová slova v angličtině

Fundamental theory of ordinary differential equations, nonuniqueness of solutions, incompatible set of conditions

Autoři

DIBLÍK, J.; NOWAK, C.

Rok RIV

2012

Vydáno

02.08.2011

ISSN

1085-3375

Periodikum

Abstract and Applied Analysis

Svazek

2011

Číslo

1

Stát

Spojené státy americké

Strany od

1

Strany do

15

Strany počet

15

Plný text v Digitální knihovně

http://hdl.handle.net/

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"
}