A Global Convergence Result with Applications to Periodic Solutions

We establish a global convergence result and then apply it to show that under appropriate hypotheses every positive solution of the difference equation xn+1=∑i=0mAixn−2i,n=0,1,…,converges to a period two solution.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2000-05, Vol.245 (1), p.161-170
Main Authors: El-Metwally, H., Grove, E.A., Ladas, G.
Format: Article
Language:English
Subjects:
Difference and functional equations, recurrence relations
Exact sciences and technology
Finite differences and functional equations
global convergence
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
periodic solutions
rational recursive sequences
Sciences and techniques of general use
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Description
Summary:We establish a global convergence result and then apply it to show that under appropriate hypotheses every positive solution of the difference equation xn+1=∑i=0mAixn−2i,n=0,1,…,converges to a period two solution.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.2000.6747