Existence for nonoscillatory solutions of higher-order nonlinear neutral difference equations. (Q1874433)

The authors give a criterion for the existence of bounded nonoscillatory solutions for a higher order nonlinear neutral difference equation. Their results extend those of \textit{F. Yang} and \textit{J. Liu} [J. Syst. Sci. Math. Sci. 22, No. 1, 85--89 (2002; Zbl 0999.39009)], \textit{Y. Zhou} [Appl. Math. Lett. 15, 785--791 (2002; Zbl 1029.39009)] and \textit{J. R. Graef} and \textit{E. Thandapani} [J. Math. Anal. Appl. 224, No. 2, 349--355 (1998; Zbl 0923.39006)]. The proofs use Krasnoselskii's fixed point theorem.