Asymptotic trichotomy for positive solutions of a class of fourth-order nonlinear neutral difference equations with quasidifferences
[ 1 ] Instytut Matematyki, Wydział Elektryczny, Politechnika Poznańska | [ P ] employee
2005
scientific article
english
- nonlinear
- neutral
- difference equation
- minimal solution
- maximal solution
- nonoscillatory solution
- quasidifferences
- fourth order
EN We consider a class of fourth-order nonlinear neutral difference equations with quasidifferences where sequence (pn) 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.
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