Large solutions to semi-linear elliptic systems with variable exponents

We consider the elliptic system Δu=uavb, Δv=ucvd where the exponents are non-negative spherically symmetric functions. We study positive solutions on balls of finite and infinite radius R which satisfy lim|x|→R⁡u(x)=lim|x|→R⁡v(x)=∞. We give conditions on the exponents that either ensure existence or nonexistence of these large solutions.