Monotone solutions of a higher-order neutral difference equation. (English) Zbl 0896.39007

Cheng, Sui Sun; Zhang, Guang

Georgian Math. J. 5, No. 1, 49-54 (1998).

The authors establish conditions for the existence of \((*)\)-monotone solutions for the neutral difference equation \[ \Delta^m (y_n- p_ny_{n-\sigma})+ q_n f(y_{n-\sigma})=0, \qquad n=0,1,2,\dots \] where \(m\) is a positive odd integer, \(\sigma\) is a positive integer, \(\{p_n\}\) and \(\{q_n\}\) are nonnegative sequences and \(f\) is a real function defined on \(\mathbb{R}\) such that \(f\) is positive nondecreasing for \(x>0\).

Reviewer: E.Thandapani (Salem)

MSC:

39A12	Discrete version of topics in analysis
39A10	Additive difference equations

Keywords:

monotone solutions; neutral difference equation