Positive solutions of nonlinear m-point boundary value problems on time scales

摘要

In this paper, by using fixed point theorems in a cone and the associated Green's function, we study the existence of at least two and three positive solutions to the m-point boundary value problem (BVP) on time scales, u(Delta del)(t) + f (t, u(t)) = 0, t is an element of [0, 1] subset of T, beta u(0) - gamma u(Delta)(0) = 0, u(1) = (m-2)Sigma(i=1) alpha(i)u(epsilon(i)), m >= 3, where T is a time scale, f is an element of C-ld([0, 1] x [0, infinity)), beta, gamma is an element of [0, infinity), alpha(i) is an element of [0, infinity) for i = 1, 2,...., m - 2, and epsilon(i) satisfy 0 < epsilon(1) < epsilon(2) < ... < epsilon(m-2) < rho(1).