Publication result detail

Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem

DIBLÍK, J.; NOWAK, C.

Original Title

Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem

English Title

Compatible and incompatible nonuniqueness conditions for the classical Cauchy problem

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

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.

English abstract

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.

Keywords

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

Key words in English

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

Authors

DIBLÍK, J.; NOWAK, C.

RIV year

2012

Released

02.08.2011

ISBN

1085-3375

Periodical

Abstract and Applied Analysis

Volume

2011

Number

1

State

United States of America

Pages from

1

Pages to

15

Pages count

15

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"
}