The boundary value problem [q(t)xΔ(t)]Δ+λf(t,xσ(t))=0,t∈[a,σ(b)]∩T,αx(a)-βxΔ(a)=0,γx(σ(b))+δxΔ(σ(b))=0 on the measure chain T is studied,where f:[a,σ(b)]×[0,∞)→[0,∞) is continuous.By using krasnoselskii fixed point theorem on cone,some conditions are imposed on f which ensure the existence of positive solution of the boundary value problem at the interval of λ.The results are extended from xΔΔ(t)+λf(t,xσ(t))=0to [q(t)xΔ(t)]Δ+λf(t,xσ(t))=0,where q(t) is bounded and positive for t∈[a,σ(b)].