Existence of entire large positive solutions of semilinear elliptic systems

We show that entire Large positive radial solutions exist for the semilinear elliptic system Delta u = p(|x|) v(alpha), Delta v = q(|x|) u(P) on R-N, N greater than or equal to 3, for positive alpha and beta, provided that the nonnegative functions p and q are continuous, c-positive, and satisfy the decay conditions integral(0)(infinity) tp(t) dt < infinity and integral(0)(infinity) tq(t) dt < infinity for alpha and beta greater than unity, and integral(0)(infinity) tq(t) dt = infinity and integral(0)(infinity) tq(t) dt = infinity if neither alpha nor beta is greater than orle. (C) 2000 Academic Press.