Existence of Positive Solution to System of Nonlinear Third-Order Three-Point BVPs

We are concerned with the following system of third-order three-point boundary value problems: u '''(t) + f(t,v(t)) = 0,t epsilon (0,1), v '''(t) + g(t,u(t)) = 0,t epsilon (0,1), u(0) = u ''(0) = 0, u'(1) = alpha u(eta), v(0) = v ''(0) = 0, and v'(1) = alpha v(eta), where < eta < 1 and 0 < alpha < 1/eta. By imposing some suitable conditions on f and g we obtain the existence of at least one positive solution to the above system. The main tool used is the theory of the fixed-point index.