Global Behavior of a Discrete Survival Model with Several Delays

Abstract

The difference equation $y_{n+1}-y_n=-\alpha y_n+{{\sum }_{j=1}^m{\beta }_{j}e}^{-{\gamma }_j{y}_{n-k_j}}$ is studied and some sufficient conditions which guarantee that all solutions of the equation are oscillatory, or that the positive equilibrium of the equation is globally asymptotically stable, are obtained.