Positive solutions for third-order boundary-value problems with the integral boundary conditions and dependence on the first-order derivatives

By using a fixed point theorem in a cone and the nonlocal third-order bvp's green function,the existence of at least one positive solution for the third-order boundary-value problem with the integral boundary conditions x ′′′ (t) + f (t,x (t),x ′ (t)) = 0,tj,x (0) = 0,x ′′ (0) = 0,and x (1) = ∫ 0 1 g (t) x (t) d t is considered,where f is a nonnegative continuous function,j = [ 0,1 ],and g l [ 0,1 ]. the emphasis here is that f depends on the first-order derivatives. © 2013 yanping guo and fei yang.