Positive Solutions for a Fourth-Order Riemann-Stieltjes Integral Boundary Value Problem

In this paper, we use the fixed point index to study the existence of positive solutions for the fourth-order Riemann-Stieltjes integral boundary value problem {-x((4)) (t) = f(t, x(t), x(t), x(t), x(t)), t is an element of(0,1) x(0) = x(0) = x(1) = 0, x(0) = alpha[x(t)] , where f: [0, 1] x R+ x R+ x R+ x R+ - R+ is a continuous function and alpha[x] denotes a linear function. Two existence theorems are obtained with some appropriate inequality conditions on the nonlinearity f, which involve the spectral radius of related linear operators. These conditions allow f(t, z(1), z(2), z(3), z(4)) to have superlinear or sublinear growth in z(i), i = 1, 2, 3, 4.