Triple positive solutions of three-point boundary value problems for fourth-order differential equations

Using the Avery and Peterson fixed point theorem, we investigate the existence of three positive solutions for the fourth order three-point boundary value problem u(0)=u(1)=0, where c1,c2,c3 and c4 are nonnegative constants satisfying c1c4+c2c3+c1c3>0, 0<ξ<1 and h(t) is sign-changing on [0,1]. The interesting point is that the nonlinear term is allowed to depend on u″.