Abstract and Applied Analysis

Abstract and Applied Analysis / 2004 / Article

Open Access

Volume 2004 |Article ID 153689 | https://doi.org/10.1155/S1085337504306056

Jaromír Baštinec, Josef Diblík, "Subdominant positive solutions of the discrete equation Δu(k+n)=p(k)u(k)", Abstract and Applied Analysis, vol. 2004, Article ID 153689, 10 pages, 2004. https://doi.org/10.1155/S1085337504306056

Subdominant positive solutions of the discrete equation Δu(k+n)=p(k)u(k)

Received08 Oct 2002

Abstract

A delayed discrete equation Δu(k+n)=p(k)u(k) with positive coefficient p is considered. Sufficient conditions with respect to p are formulated in order to guarantee the existence of positive solutions if k. As a tool of the proof of corresponding result, the method described in the author's previous papers is used. Except for the fact of the existence of positive solutions, their upper estimation is given. The analysis shows that every positive solution of the indicated family of positive solutions tends to zero (if k) with the speednot smaller than the speed characterized by the function k·(n/(n+1))k. A comparison with the known results is given and some open questions are discussed.

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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