Asymptotic trichotomy for positive solutions of a class of fourth-order nonlinear neutral difference equations with quasidifferences

We consider a class of fourth-order nonlinear neutral difference equations with quasidifferences where sequence (p(n)) is uniformly strictly subnormal. The classification of nonoscillatory solutions of this equation are obtained. The conditions under which the eventually positive solutions of considered equation can be classified into three nonempty distinct categories are given. Sufficient conditions are obtained for the difference equation to admit the existence of a minimal solutions. Also necessary and sufficient conditions are obtained for the difference equation to admit the existence of an asymptotically constant and a maximal solutions. Results are illustrated on examples. (C) 2005 Elsevier Ltd. All rights reserved.