Large solutions to non-monotone semilinear elliptic systems

We present the existence of entire large positive radial solutions for the non-monotonic system Δ u = p ( | x | ) g ( v ) , Δ v = q ( | x | ) f ( u ) on R n where n ⩾ 3 . The functions f and g satisfy a Keller–Osserman type condition while nonnegative functions p and q are required to satisfy the decay conditions ∫ 0 ∞ t p ( t ) d t < ∞ and ∫ 0 ∞ t q ( t ) d t < ∞ . Further, p and q are such that min ( p , q ) does not have compact support.