# zbMATH — the first resource for mathematics

Note on the behavior of solutions of difference equations of arbitrary order. (English) Zbl 0887.39004
Let $$f:\mathbb{R}\to \mathbb{R}$$ satisfy $$xf(x)>0$$ for $$x\neq 0$$. Let $$\tau_n$$ be a sequence of integers satisfying $$\tau_n<n$$ and $$\tau\to\infty$$ when $$n\to\infty$$. The author studies qualitative properties of the solution of the nonlinear difference equation $\Delta^m(u_n+p_nu_{n-k})+q_nf(u_{\tau_n})=0,\qquad m\geq 1,\quad n=0,1,2,\dots,$ where $$\{p_n\}$$ and $$\{q_n\}$$ are real sequences and $$k$$ is a positive integer.
##### MSC:
 39A12 Discrete version of topics in analysis 39A10 Additive difference equations