ON THIRD-ORDER THREE-POINT RIGHT FOCAL BOUNDARY VALUE PROBLEMS

In this paper, a fixed point theorem in a cone, some inequalities of the associated Green's function and the concavity of solutions are applied to obtain the existence of positive solutions of third-order three-point boundary value problem with dependence on the first-order derivative x"' (t) = f (t, x(t), x' (t)), 0 < t < 1, x(0) = x' (eta) = x" (1) = 0, where f : [0, 1] x [0, infinity) x R -> [0, infinity) is a nonnegative continuous function, eta is an element of(1/2,1).