Positive solutions for multipoint boundary value problems with one-dimensional p-Laplacian operator

In this paper, we study the existence of positive solutions for the following nonlinear m-point boundary value problem with p-Laplacian:(ϕp(u′))′+a(t)f(u(t))=0,0 1, ϕq=(ϕp)-1,1p+1q=1, 1 ⩽ k ⩽ s ⩽ m − 2, ai, bi ∈ (0, +∞) with 0<∑i=1kbi-∑i=k+1sbi<1,0<∑i=1m-2ai<1,0<ξ1<ξ2<⋯<ξm-2<1, a(t) ∈ C((0, 1), [0, +∞)), f ∈ C([0, +∞), [0, +∞)) . We show that there exists one or two positive solutions by using fixed-point theorem for operator on a cone. The conclusions in this paper essentially extend and improve the known results.