ON THE EXISTENCE OF POSITIVE SOLUTIONS FOR THE ONE-DIMENSIONAL p-LAPLACIAN BOUNDARY VALUE PROBLEMS ON TIME SCALES

In this paper, we study the following p-Laplacian boundary value problems on time scales ( (φp(u ∆(t)))∇ + a(t)f(t, u(t), u∆(t)) = 0, t ∈ [0, T ]T, u(0) − B0(u ∆(0)) = 0, u∆(T ) = 0, where φp(u) = |u| p−2u, for p > 1. We prove the existence of triple positive solutions for the onedimensional p-Laplacian boundary value problem by using the Leggett-Williams fixed point theorem. The interesting point in this paper is that the non-linear term f is involved with first-order derivative explicitly. An example is also given to illustrate the main result.