Large solutions to semi-linear elliptic systems with variable exponents

We consider the elliptic system Δ u = u a v b , Δ v = u c v d 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.