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"
}