Positive solutions of higher-order nonlinear delay difference equations (Q1827179)

The authors study the nonlinear difference equation \[ \Delta^m x_{n-1} \pm f(n, x_{n-\tau}) = 0, \] where \(m \geq 2\) and \(f\) is a real-valued continuous function with \(f(n,x) \geq 0\) for \(x > 0\). They classify positive solutions according to their asymptotic behavior and under the assumption that \(f(n,x)\) is non-decreasing or non-increasing in \(x\).