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

Abstract

In this paper, we study the following p-Laplacian boundary value problems on time scales

{(phi(p)(u(Delta)(t)))(del) + a(t)f(t, u(t), u(Delta)(t)) = 0, t is an element of [0,T](T),

u(0) - B-0(u(Delta)(0)) = 0, u(Delta)(T) = 0,

where phi(p)(u) = vertical bar u vertical bar(p-2)u, for p > 1. We prove the existence of triple positive solutions for the one-dimensional 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.