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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.

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