Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4623170 | Journal of Mathematical Analysis and Applications | 2007 | 4 Pages |
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
Authors
Taixiang Sun, Hongjian Xi,