Existence of Positive Solutions for a Fourth-Order Periodic Boundary Value Problem

The existence results of positive solutions are obtained for the fourth-order periodic boundary value problem u((4)) - beta u '' + alpha u = f(t, u, u ''), 0 <= t <= 1, u((i))(0) = u((i))(1), i = 0, 1, 2, 3, where f : [0, 1] x R(+) x R -> R(+) is continuous, alpha, beta is an element of R, and satisfy 0 < alpha < ((beta/2) + 2 pi(2))(2), beta > -2 pi(2), (alpha/pi(4)) + (beta/pi(2)) + 1 > 0. The discussion is based on the fixed point index theory in cones.