The multiple positive solutions for p-Laplacian multipoint BVP with sign changing nonlinearity on time scales

In this paper, we consider the following p-Laplacian multipoint boundary value problem on time scales: φp u (t) ∇ +a(t)f t,u(t) = 0, t∈ [0,T ]T, φp u (0) = n −2 i=1 aiφp u (ξi ) , u(T) = n −2 i=1 biu(ξi ), where φp(s) = |s|p−2s, p > 1, ξi ∈ [0,T ]T, 0 < ξ1 < ξ2 < · · · < ξn−2 < ρ(T). By using fixed point index, we provide some sufficient conditions for the existence of multiple positive solutions to the above boundary value problem. Especially, the nonlinear term f (t,u) is allowed to change sign. As an application, an example is given to demonstrate our result. © 2008 Elsevier Inc. All rights reserved.