Solvability of a Second Order Nonlinear Neutral Delay Difference Equation - Zeqing Liu; Liangshi Zhao; Jeong Sheok Ume; Shin Min Kang (Abstract and Applied Analysis)
This paper studies the second-order nonlinear neutral delay difference equation Δ[anΔ(xn+bnxn−τ)+f(n,xf1n,…,xfkn)]+g(n,xg1n,…,xgkn)=cn, n≥n0. By means of the Krasnoselskii and Schauder fixed point theorem and some new techniques, we get the existence results of uncountably many bounded nonoscillatory, positive, and negative solutions for the equation, respectively. Ten examples are given to illustrate the results presented in this paper.