Positive Nonlinear difference equations - Some results and applications

Given a non-autonomous k-th order difference equation Un+k = f(n)(u(n),...,u(n+k-1)), n = 0,1,2,..., positivity means that for each number 71 the mapping fn is non-negative for all u(n),...,u(n+k-1) greater than or equal to 0. This article reports on results about the global asymptotic behavior of the solutions (u(n))(ngreater than or equal to0) of this equation for the autonomous case (i.e. f(n) = f for all n) as well as for the non-autonomous case. Some results and applications are presented on global asymptotic stability (autonomous case) and limit set trichotomy (non-autonomous case).