Abstract
We study the oscillatory behavior, the periodicity and the asymptotic behavior of the positive solutions of the system of two nonlinear difference equations xn+1 = A + xn−1/yn and yn+1 = A + yn−1/xn, where A is a positive constant, and n = 0, 1, ….
Highlights
In [3] Kulenovic, Ladas and Sizer studied the global stability character and the periodic nature of the positive solutions of the difference equation xn+1 =αxn + βxn−1, γxn + δxn−1 n = 0, 1, . . . , (1.1)where α, β, γ, δ are positive constants and x−1, x0 > 0
First we find conditions so that a positive solution of system (1.3) oscillates about (μ1, μ2)
In the first proposition we study the oscillatory behavior of the positive solutions of (1.3)
Summary
We find conditions so that a positive solution of system (1.3) tends to (μ1, μ2) as n → ∞. A positive solution (xn, yn) of system (1.3) oscillates about (μ1, μ2) if there exists an s ∈ {0, 1, . In the following proposition we study the existence of period 2 solutions of (1.3). In the following proposition we find positive solutions of system (1.3) which tend to (μ1, μ2) as n → ∞.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematics and Mathematical Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
