Existence of uncountably many bounded positive solutions for second order nonlinear neutral delay difference equations

This paper deals with the second order nonlinear neutral delay difference equation Δ[a(n)Δ(x(n)+b(n)x(n−τ)−c(n))]+f(n,x(f1(n)),x(f2(n)),…,x(fk(n)))=d(n),n≥n0. By using Krasnoselskii’s fixed point theorem and some new techniques, we obtain the existence results of uncountably many bounded positive solutions for the above equation. Examples that cannot be solved by known results are given to illustrate the results presented in this paper.