Positive solutions of singular p-Laplacian dynamic equations with sign changing nonlinearity

Let T be a time scale such that 0, T is an element of T. By the Schauder fixed-point theorem and the upper and lower solution method, we present some existence criteria of the positive solution of m-point singular p-Laplacian dynamic equation (phi(p)(u(Delta)(t)))(del) + q(t)f(t, u(t)) = 0, t is an element of (0, T)(inverted perpendicular) with boundary conditions u(0) = 0, (m-1)Sigma(i=1)psi(i)(u(xi(i))) + u(Delta)(T) = 0, m >= w, where phi(p)(s) = vertical bar s vertical bar(p-2) with p > 1, chi(i): R -> R is continuous for i = 1, 2, ..., m - 1 and nonincreasing if m >= 3, 0 < xi(1) < xi(2) < ... < xi(m - 2) < xi(m - 1) = T. The nonlinear term may be singular in its dependent variable and is allowed to change sign. Our results are new even for the corresponding differential (T = R) and difference equations (T = Z). As an application, an example is given to illustrate our result. (C) 2007 Elsevier Inc. All rights reserved.