POSITIVE SOLUTIONS OF NONLINEAR ELLIPTIC-SYSTEMS

In this paper we prove the existence of nonnegative and non-trivial solutions of problems of the form -DELTAu(x) = u(x)f(x, u(x), v(x)), x is-an-element-of OMEGA, -DELTAv(x) = v(x)g(x, u(x), v(x)), x is-an-element-of OMEGA, u(x) = v(x) = 0, x is-an-element-of partial derivativeOMEGA. Our main result improves many previous results Of other authors and it may be applied to study the three standard situations: competition, prey-predator and cooperative models. We also cover some other cam which, due essentially to the spatial dependence or to a nonlinear interaction, we not any of these three types. The method of proof combines a decoupling method with a global bifurcation result.