The discrete Φ-Laplacian boundary problem 〖JB({〗〖HL(1〗Δ((Δu(k－1)))+λp(k)f(u(k))=0

k∈{1

2

…

T}

u(0)=u(T+1)=0〓〓〓〓〓〓〓〓〖HL)〗〖JB)〗  is studied

where T>5 is a given positive integer

λ is a nonnegative parameter and Φ is an odd and increasing homeomorphism from 〖WTHZ〗R〖WTBZ〗 onto 〖WTHZ〗R〖WTBZ〗. Applying the fixed point theorem in cones

it is proved under the weakened condition liminf〖DD(X〗u→∞〖DD)〗〖SX(〗f(u)〖〗(u)〖SX)〗∈(0

∞］ that the problem has at least one positive solution for λ belonging to an explicit open interval.