Triple Positive Solutions of the Multi-Point Boundary Value Problem for Second-Order Differential Equations

We consider the second-order differential equation u(t) + q(t)f(t,u(t),u (t)) = 0,0 < t < 1,subject to three-point boundry condition u(0) = 0,u(1) = a 0 u(ξ 0 ),or to m-point boundary conditionu (0) = m2 i=1 b i u (ξ i ),u(1) = m2 i=1 a i u(ξ i ).We show the existence of at least three positive solutions of the above multi-point boundary-value problem by applying a new fixed-point theorem introduced by Avery and Peterson.