Asymptotic representations of solutions of k-th order Emden–Fowler difference equation

Abstract

In this paper we establish the asymptotical representations of solutions of k-th order Emden–Fowler difference equation where p(n) is close to a power sequence. We obtained the necessary conditions for the existence of solutions and we also found the sufficient conditions of their existence for non-critical classes. These results are generalizations of corresponding theorems for second-order Emden–Fowler equation.