Detail publikace

# Retract principle for difference equations.

Originální název

Retract principle for difference equations.

Anglický název

Retract principle for difference equations.

Jazyk

en

Originální abstrakt

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.

Anglický abstrakt

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.

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"
}``````