Multiple positive solutions of nonlinear third-order BVP for a class of p-Laplacian dynamic equations on time scales

In this paper, by using fixed-point theorems in cones, the existence of multiple positive solutions is considered for singular nonlinear boundary value problem for the following third-order p-Laplacian dynamic equations on time scales. (Phi(p)(u(Delta Delta)(t)))(del) + f (t, u(t)) = 0, t epsilon [a, b], alpha u(rho(a)) = beta u(Delta)(rho(a)) = 0, gamma u(b) + delta u(Delta)(b) = 0, u(Delta Delta)(rho(a)) = 0, where Phi(p)(s) is p-Laplacian operator, i. e., Phi(p)(s) = vertical bar s vertical bar(p-2) s, p > 1, Phi(-1)(p) = Phi(q), 1/p + 1/q = 1. In particular, the conditions we used in the paper are different from those in [ R. Y. Ma, Existence of solutions of nonlinear m-point boundary value problem, J.Math.Anal.Appl. 256 (2001) 556-567; A.M. Mao, S.X. Luan, Y.H. Ding, On the existence of positive solutions for a class of singular boundary value problems, J.Math.Appl. 298 (2004) 57-72]. (C) 2008 Elsevier Ltd. All rights reserved.