POSITIVE SOLUTIONS FOR A SYSTEM OF NONLINEAR BOUNDARY-VALUE PROBLEMS ON TIME SCALES

We determine the values of a parameter lambda for which there exist positive solutions to the system of dynamic equations u(Delta Delta)(t) + lambda p(t)f(v(sigma(t))) = 0, t is an element of [a, b](T), v(Delta Delta)(t) + lambda q(t)g(u(sigma(t))) = 0, t is an element of [a, b](T), with the boundary conditions, alpha u(a)-beta u(Delta)(a) = 0, gamma u(sigma(2)(b))+ delta u(Delta)(sigma(b)) = 0, alpha v(a) - beta v(Delta)(a) = 0, gamma v(sigma(2)(b)) + delta v(Delta)(sigma(b)) = 0, where T is a time scale. To this end we apply a Guo-Krasnosel'skii fixed point theorem.