Existence of Entire Large Positive Solutions of Semilinear Elliptic Systems

We show that entire large positive radial solutions exist for the semilinear elliptic system Δu=p(x) vα, Δv=q(x) uβ on RN, N 3, for positive α and β, provided that the nonnegative functions p and q are continuous, c-positive, and satisfy the decay conditions ∫∞0 tp(t) dt<∞ and ∫∞0 tq(t) dt<∞ for α and β greater than unity, and ∫∞0 tp(t) dt=∞ and ∫∞0 tq(t) dt=∞ if neither α nor β is greater than one.