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Title: One case of appearance of positive solutions of delayed discrete equations (English)
Author: Baštinec, Jaromír
Author: Diblík, Josef
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 48
Issue: 6
Year: 2003
Pages: 429-436
Summary lang: English
Category: math
Summary: When mathematical models describing various processes are analysed, the fact of existence of a positive solution is often among the basic features. In this paper, a general delayed discrete equation \[ \Delta u(k+n)=f(k,u(k),u(k+1),\dots ,u(k+ n)) \] is considered. Sufficient conditions concerning $f$ are formulated in order to guarantee the existence of a positive solution for $k\rightarrow \infty $. An upper estimate for it is given as well. The appearance of the positive solution takes its origin in the nature of the equation considered since the results hold only for delayed equations (i.e. for $n>0$) and not for the case of an ordinary equation (with $n=0$). (English)
Keyword: positive solution
Keyword: nonlinear discrete delayed equation
MSC: 39A10
MSC: 39A11
MSC: 39A12
idZBL: Zbl 1099.39001
idMR: MR2025296
DOI: 10.1023/B:APOM.0000024484.15065.1c
Date available: 2009-09-22T18:14:59Z
Last updated: 2020-07-02
Stable URL:
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