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The present research investigates the following delayed problem (0.1) ν′′+a(t)f(t,νt)=0,0<t<1,ν(t)=ϕ(t),−τ≤t≤0,ν′(0)=0,ν(1)=αν(γ)+βν′(γ),0≤γ≤1,0≤ξ<1,0≤υ≤ξ(1−γ),Using kranoselskii fixed point theorem on cones, and the fixed point index theory, we will show the existence of positive solutions for the problem. Also the multiplicity is shown.