Existence of entire large positive solutions of a semilinear elliptic system (Q1883526)

The authors show existence of large positive radial solutions to the semilinear system \[ \begin{cases} \Delta u=p(| x| )f(v), & \\ \Delta v=q(| x| )g(u), & x\in {\mathbb R}^N,\quad N\geq 3 \end{cases} \] for nonnegative, nondecreasing continuous functions \(f\) and \(g,\) and nonnegative, continuous and \(C\)-positive functions \(p\) and \(q\) satisfying the decay estimates \[ \int_0^\infty tp(t)\,dt<\infty,\qquad \int_0^\infty tq(t)\,dt<\infty, \] \[ \int_1^\infty \left[\int_0^s f(t)\,dt\right]^{-1/2}\,ds<\infty,\qquad \int_1^\infty \left[\int_0^s g(t)\,dt\right]^{-1/2}\,ds<\infty. \]