Solvability of a fourth-order boundary value problem with integral boundary conditions

We investigate the existence of solutions and positive solutions for a nonlinear fourth-order differential equation with integral boundary conditions of the form x (4) (t) = f (t,x (t),x ′ (t),x ′ ′ (t),x ′ ′ ′ (t)),t [ 0,1 ],x (0) = x ′ (1) = 0,x ′ ′ (0) = ∫ 0 1 h (s,x (s),x ′ (s),x ′ ′ (s)) d s,x ′ ′ ′ (1) = 0,where f c ([ 0,1 ] × 4),h c ([ 0,1 ] × 3). by using a fixed point theorem due to d. o'regan,the existence of solutions and positive solutions for the previous boundary value problems is obtained. meanwhile,as applications,some examples are given to illustrate our results. © 2013 hui li et al.