Entire Large Solutions to Semilinear Elliptic Systems of Competitive Type

We consider the elliptic system Delta u=p(P vertical bar x vertical bar)u(a)P(b), Delta v=q(vertical bar x vertical bar)u(c)v(d) on R-n (n >= 3) where a, b, c, d are nonnegative constants with max{a,d} <= 1, and the functions p and q are nonnegative, continuous, and the support of min{p(r),q(r)} is not compact. We establish conditions on p and q, along with the exponents a, b, c, d, which ensure the existence of a positive entire solution satisfying lim(vertical bar x vertical bar ->infinity)u(x)= lim(vertical bar x vertical bar ->infinity)(x)=infinity.