Abstract
In this paper, we establish asymptotic representations of positive solutions of the Emden–Fowler difference equation , where p n is ‘close’ to a power sequence. In particular, for some types of p n and σ asymptotic behaviours of all solutions of the equation are determined. The proof of the main result is based on the idea of comparison of an arbitrary positive solution of the Emden–Fowler equation with a special sequence in order to estimate the rate of growth of this solution.
Notes
1. If the upper index of summing equals zero then we put that the sum equals zero.