Oscillatory and asymptotic properties of higher order nonlinear neutral difference equations

In this paper, we study the oscillatory and asymptotic properties of solutions of higher order nonlinear neutral difference equations. Using Krasnoselskii's fixed point theorem, Schauder's fixed point theorem and Lebesgue's dominated convergence theorem, we obtain some necessary and sufficient conditions for all bounded solutions to be oscillatory or tend to zero. Our results extend and improve some known results.