Oscillation and asymptotic behaviour of a class of higher-order non-linear difference equations (Q2568773)

The main mathematical object of the paper is the difference equation \[ x_{n+1} = f_1(x_{n-\tau_1}) + f_2(x_{n-\tau_2}) \] with \(f_i(\cdot)>0\) continuous functions globally defined on \(R_+\) and \(\tau_i\) nonnegative integers such that e.g. \(\tau_1\leq\tau_2\). Some monotonicity and growth assumptions are also made as natural extensions of population models. The paper discusses attractivity of equilibria and oscillation of the solutions.