EXISTENCE OF POSITIVE ENTIRE SOLUTIONS FOR WEAKLY COUPLED SEMILINEAR ELLIPTIC-SYSTEMS

Weakly coupled semilinear elliptic systems of the form [GRAPHICS] are considered in R(N), N greater-than-or-equal-to 2, where k = 1, 2, ..., M, u = (u1, ..., u(M)) and lambda is a real constant. The aim of this paper is to give sufficient conditions for (*) to have entire solutions whose components are positive in R(N) and converge to non-negative constants as \x\ tends to infinity. For this purpose a new supersolution-subsolution method is developed for the system (*) without any hypotheses on the monotonicity of the non-linear terms f(k) with respect to u.