TRIPLE POSITIVE SOLUTIONS FOR SYSTEM OF NONLINEAR SECOND-ORDER THREE POINT BOUNDARY VALUE PROBLEM

In this work, we apply the Legget-Williams fixed point theorems to obtain sufficient condition for the existence of at least three positive solutions of boundary value problems for systems of second-order ordinary differential equations of the form {-u(n)(t) + k(2)u(t) = f(t, u(t), v(t)), 0 < t < 1, -v(n)(t) + omega(2)v(t) = f(t, u(t), v(t)), 0 < t < 1, u(0) = v(0) = 0, u(1) = beta u(eta), v(1) = lambda v(n), where f : (0, 1) x [0, +infinity) x [0, +infinity) -> [0, +infinity); g : [0, 1] x [0, +infinity) x [0, +infinity) -> [0, +infinity) and k, omega are positive constants, 0 < eta < 1, 0 < ss < ss(0), 0 < lambda < lambda(0.)