Positive solutions of M-point boundary value problem for second-order dynamic equations on time scales

摘要

This paper deals with the existence of multiple positive solutions for second-order dynamic equations on time scales u(Delta del) + f(t, u(t)) = 0, t is an element of (0, T) subset of T, with multi-point boundary conditions u(0) = 0, u(T) = Sigma(m-2)(i-1)k(i)u(xi(i)), where T is a time scale, k(i) > 0 (i = 1, ..., m - 2), 0 < xi(1) < xi(2) < ... < xi(m-2) < rho(T), 0 < Sigma(m-2)(i=1)k(i)xi(i) < T. By using Green's function and the Leggett-Williams fixed point theorem in an appropriate cone, the existence of at least three positive solutions of the problem is obtained.