The author investigates a class of difference equations of type
for , which includes a large class of mathematical biology models, such as the generalized Beverton-Holt stock recruitment model, the flour beetle population model, a mosquito population equation, and a discrete delay logistic difference equation. The main result shows that for ,
for , where , are homogeneous polynomials of second and third order respectively, and moreover is a positive definite form. Then there exists a positive solution of with the following asymptotics:
where and are constants.