A necessary and sufficient condition for the existence of large solutions to sublinear elliptic systems

We prove that the elliptic system Δu=p(|x|)vαΔu=p(|x|)vα, Δv=q(|x|)uβΔv=q(|x|)uβ on RnRn (n⩾3n⩾3) where 0<α⩽10<α⩽1, 0<β⩽10<β⩽1, and p and q   are nonnegative continuous functions has a nonnegative entire radial solution satisfying lim|x|→∞u(x)=lim|x|→∞v(x)=∞lim|x|→∞u(x)=lim|x|→∞v(x)=∞ if and only if the functions p and q satisfy∫0∞tp(t)(t2−n∫0tsn−3Q(s)ds)αdt=∞,∫0∞tq(t)(t2−n∫0tsn−3P(s)ds)βdt=∞ with P(r)=∫0rτp(τ)dτ and Q(r)=∫0rτq(τ)dτ. This extends previous existence results for both the single equation and systems.