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

Abstract

In this paper we establish the asymptotical representations of PðlÞ solutions of k-th order Emden -Fowler difference equationi¼0 jD i y nþsi j si signðy nþs0 Þ; where p n is close to a power sequence. We obtained the necessary conditions for the existence of PðlÞ 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.

Decaying solutions for discrete boundary value problems on the half line

“…Discrete boundary value problems (BVPs), associated to equations of type (1), have attracted considerable attention in the last years, especially when they are examined on unbounded domains, see, e.g., [2,4,5,10,11,18,20], the monographies [1,3] and references therein. Equation (1) appears in the discretization process for searching spherically symmetric solutions of certain nonlinear elliptic di¤erential equations with p-Laplacian, see, e.g., [13].…”