Detail publikačního výsledku

Retract principle for difference equations.

DIBLÍK, J.

Originální název

Retract principle for difference equations.

Anglický název

Retract principle for difference equations.

Druh

Stať ve sborníku v databázi WoS či Scopus

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.

Klíčová slova

Retract principle, difference equations.

Klíčová slova v angličtině

Retract principle, difference equations.

Autoři

DIBLÍK, J.

Vydáno

21.03.1998

Nakladatel

Gordon and Breach Science Publishers, Holandsko

ISBN

90-5699-688-6

Kniha

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

Edice

1

Strany od

107

Strany do

115

Strany počet

9

BibTex

@inproceedings{BUT2126,
  author="Josef {Diblík}",
  title="Retract principle for difference equations.",
  booktitle="Communications n Difference equations, Proceedings of the Fourth International Conference on Differential Equations",
  year="1998",
  series="1",
  number="1",
  pages="107--115",
  publisher="Gordon and Breach Science Publishers, Holandsko",
  isbn="90-5699-688-6"
}