Article ID Journal Published Year Pages File Type
4623170 Journal of Mathematical Analysis and Applications 2007 4 Pages PDF
Abstract

In this note we study the difference equationxn+1=1+xn−1xn,n=0,1,…, where initial values x−1,x0∈(0,+∞)x−1,x0∈(0,+∞), and obtain the set of all initial values x−1,x0∈(0,+∞)x−1,x0∈(0,+∞) such that the positive solutions {xn}n=−1∞ of that equation converges to the unique equilibrium x¯=2. This answers the open problem 4.8.9 proposed by M.R.S. Kulenovic and G. Ladas in [M.R.S. Kulenovic, G. Ladas, Dynamics of Second Order Rational Difference Equations, with Open Problems and Conjectures, Chapman and Hall/CRC, 2002].

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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