Large solutions to non-monotone semilinear elliptic systems

We present the existence of entire large positive radial solutions for the non-monotonic system Δu=p(|x|)g(v), Δv=q(|x|)f(u) on Rn 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 and . Further, p and q are such that min(p,q) does not have compact support.