×

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
PDF BibTeX XML Cite