Article ID Journal Published Year Pages File Type
6421396 Applied Mathematics and Computation 2013 8 Pages PDF
Abstract

We investigate the boundedness of positive solutions of the reciprocal max-type difference equationxn=maxAn-11xn-1,An-12xn-2,⋯,An-1txn-t,n=1,2,…,where, for each value of i, the sequence Anin=0∞ of positive numbers is periodic with period pi. We give both sufficient conditions on the pi's for the boundedness of all solutions and sufficient conditions for all solutions to be unbounded. This work essentially complements the work by Bidwell and Franke, who showed that as long as every positive solution of our equation is bounded, then every positive solution is eventually periodic, thereby leaving open the question as to when solutions are bounded.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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