Positive solutions of a fourth-order differential equation with integral boundary conditions

We study the existence of positive solutions to the fourth-order two-point boundary value problem ( u''''(t) + f (t, u(t)) = 0, 0 < t < 1, u'(0) = u'(1) = u''(0) = 0, u(0) = alpha[u], where alpha[u] = integral(1) (0) u(t)dA(t) is a Riemann-Stieltjes integral with A > 0 being a nondecreasing function of bounded variation and f epsilon C ([0, 1] xR(+), R+). The sufficient conditions obtained are new and easy to apply. Their approach is based on Krasnoselskii's fixed point theorem and the Avery-Peterson fixed point theorem.