摘要：This paper studies higher-order nonlinear neutral delay difference equations of the form Δ ( r n m − 1 ( Δ ( r n m − 2 ( ⋯ ( Δ ( r n 1 ( Δ ( x n + p n x n − τ ) ) γ 1 ) ) γ 2 ⋯ ) γ m − 2 ) ) γ m − 1 ) = f ( n , x n − τ 1 , … , x n − τ s ) . $$\begin{aligned}& \varDelta \bigl(r^{m-1}_{n} \bigl(\varDelta \bigl(r^{m-2}_{n} \bigl(\cdots \bigl(\varDelta \bigl(r^)_{n} \bigl( \varDelta (x_{n}+p_{n}x_{n-\tau}) \bigr)^{\gamma_)} \bigr) \bigr)^{\gamma_,}\cdots \bigr)^{\gamma _{m-2}} \bigr) \bigr)^{\gamma_{m-1}} \bigr)\\& \quad = f(n,x_{n-\tau_)},\ldots,x_{n-\tau_{s}}). \end{aligned}$$ Using Krasnoselskii’s fixed point theorem, we obtain the existence of uncountably many bounded positive solutions to the considered problem.
关键词：nonlinear difference equation ; neutral type ; Krasnoselskii’s fixed point theorem
