Positive Solutions To Systems Of Nonlinear Second-Order Three-Point Boundary Value Problems

In this paper, we investigate the following system of nonlinear second-order three-point boundary value problem { -u '' = f(t, v), t epsilon (0, 1), -v '' = g(t, u) t epsilon (0, 1), u(0) = alpha u(eta), u(1) = beta u(eta), v(0) = alpha v(eta), v(1) = beta v(eta), where eta epsilon (0, 1) and 0 < beta <= alpha < 1. Green's function for the associated linear boundary value problem is constructed, and several useful properties of the Green's function are obtained. Existence and multiplicity criteria of positive solutions are established by using the well-known fixed point theorems of cone expansion and compression.