Publication detail

# Retract principle for difference equations.

DIBLÍK, J.

Original Title

Retract principle for difference equations.

English Title

Retract principle for difference equations.

Type

conference paper

Language

en

Original Abstract

A power tool for investigation of various problems for ordinary differential equations as well as delayed differential equations is a retraction method. The developing of this method is discussed in the case of one scalar difference equation. The definition of the point of the type of strict egress for a given set with respect to the difference equation $\Delta u(k)= f(k,u(k))$ is involved. For this equation the conditions for existence of at least one solution with graph remaining in a given set are formulated. The proof is based on the idea of a retract principle. In construction of a retract mapping the property of continuous dependence of solutions on their initial data is used. Illustrative examples are considered too.

English abstract

A power tool for investigation of various problems for ordinary differential equations as well as delayed differential equations is a retraction method. The developing of this method is discussed in the case of one scalar difference equation. The definition of the point of the type of strict egress for a given set with respect to the difference equation $\Delta u(k)= f(k,u(k))$ is involved. For this equation the conditions for existence of at least one solution with graph remaining in a given set are formulated. The proof is based on the idea of a retract principle. In construction of a retract mapping the property of continuous dependence of solutions on their initial data is used. Illustrative examples are considered too.

Keywords

Retract principle, difference equations.

RIV year

2000

Released

21.03.1998

Publisher

Gordon and Breach Science Publishers, Holandsko

ISBN

90-5699-688-6

Book

Communications n Difference equations, Proceedings of the Fourth International Conference on Differential Equations

Edition

1

Edition number

1

Pages from

107

Pages to

115

Pages count

9

Documents

BibTex

```
@inproceedings{BUT2126,
author="Josef {Diblík}",
title="Retract principle for difference equations.",
annote="A power tool for investigation of various problems for ordinary differential equations as well as delayed differential equations is a retraction method. The developing of this method is discussed in the case of one scalar difference equation. The definition of the point of the type of strict egress for a given set with respect to the difference equation $\Delta u(k)= f(k,u(k))$ is involved. For this equation the conditions for existence of at least one solution with graph remaining in a given set are formulated. The proof is based on the idea of a retract principle. In construction of a retract mapping the property of continuous dependence of solutions on their initial data is used. Illustrative examples are considered too.",
address="Gordon and Breach Science Publishers, Holandsko",
booktitle="Communications n Difference equations, Proceedings of the Fourth International Conference on Differential Equations",
chapter="2126",
edition="1",
institution="Gordon and Breach Science Publishers, Holandsko",
year="1998",
month="march",
pages="107--115",
publisher="Gordon and Breach Science Publishers, Holandsko",
type="conference paper"
}
```