Existence of positive solutions of discrete linear equations with a single delay

In the paper, we use a classical comparison result to prove the existence of positive solutions to a particular and very frequently investigated class of linear difference equations with a positive coefficient and a single delay. The relevant result is given in the form of an inequality (with a suit...

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Bibliographic Details
Published in:Journal of difference equations and applications 2010-09, Vol.16 (9), p.1047-1056
Main Authors: Bastinec, J, Diblík, J, Smarda, Z
Format: Article
Language:English
Subjects:
asymptotic behaviour
Comparative analysis
Differential equations
discrete delayed equation
Mathematical analysis
Mathematical functions
oscillating solution
positive solution
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Summary:In the paper, we use a classical comparison result to prove the existence of positive solutions to a particular and very frequently investigated class of linear difference equations with a positive coefficient and a single delay. The relevant result is given in the form of an inequality (with a suitable auxiliary comparison function) for the equation coefficient. A parallel to known results is included as well as a discussion of future directions.
ISSN:1023-6198
1563-5120
DOI:10.1080/10236190902718026