Uncountably many solutions of a third order nonlinear difference equation with neutral delay

In this paper, by using the Schauder fixed point theorem, Krasnoselskii fixed point theorem and some new techniques, we obtain the existence of uncountably many solutions for a third order nonlinear difference equation with neutral delay of the form ∆ ( a(n, xa1n , xa2n , . . . , xarn)∆ (xn + bnxn−τ ) ) + ∆h ( n, xh1n , xh2n , . . . , xhkn ) + f ( n, xf1n , xf2n , . . . , xfkn ) = cn, n ≥ n0. The results presented improve and generalize some results in literatures. Seven examples are given to illustrate the results presented in this paper. c ©2016 All rights reserved.