Existence of entire explosive positive radial solutions for a class of quasilinear elliptic systems. (Q1419749)

The author considers the following quasilinear elliptic system \[ \begin{aligned} \text{div}(|\nabla u|^{m-2}\nabla u) &= p(| x|) g(v),\\ \text{div}(|\nabla v|^{n-2}\nabla v) &= q(| x|) f(u),\end{aligned}\tag{1} \] where \(N\geq 3\), \(m> 1\), \(n> 1\) and \(p,q\in C(\mathbb{R}^N)\) are positive functions. The author is mainly interested in the existence of entire explosive positive functions of (1), that is positive solutions that satisfy \(u(x)\to \infty\) and \(v(x)\to\infty\) as \(| x|\to \infty\). Under suitable assumptions on \(f\), \(g\) the author proves existence of entire explosive positive radial solutions for (1).