We consider the multi-point discrete boundary value problem with one-dimensional p-Laplacian operator Δ φp Δu t − 1 q t f t, u t ,Δu t 0, t ∈ {1, . . . , n − 1} subject to the boundary conditions: u 0 0, u n ∑m−2 i 1 aiu ξi , where φp s |s|p−2s, p > 1, ξi ∈ {2, . . . , n − 2} with 1 < ξ1 < · · · < ξm−2 < n − 1 and ai ∈ 0, 1 , 0 < ∑m−2 i 1 ai < 1. Using a new fixed point theorem due to Avery and...