Multiple positive solutions for multipoint boundary value problems with sign changing nonlinearity

In this paper, we consider the multipoint boundary value problem for one-dimensional p-Laplacian(ϕp(u′))′+q(t)f(t,u)=0,t∈(0,1),subject to the boundary value conditions:u(0)=∑i=1nαiu(ξi),u(1)=∑i=1nβiu(ξi),where ϕp(s) = ∣s∣p−2s, p > 1, ξi∈(0,1)ξi∈(0,1) with 0<ξ1<ξ2<⋯<ξn<10<ξ1<ξ2<⋯<ξn<1 and αi,βi∈[0,∞)αi,βi∈[0,∞) satisfy 0<∑i=1nαi,∑i=1nβi<1. The nonlinear term f may change sign. Using a fixed point theorem for operators in a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.