Solutions with radial symmetry for a semilinear elliptic system with weights (Q1680037)

The author considers the semilinear elliptic system \[ \begin{cases} \Delta u = p_1(|x|)f(u,v), & x \in\mathbb R^N, \\ \Delta v = p_2(|x|)g(u), & x \in\mathbb R^N \end{cases}, \] where \(N \geq 3\), \(f\in C([0,\infty)\times[0,\infty))\), \(g \in C[0,\infty)\), \(f(s,t)\geq 0\) for \(s\geq 0\) and \(t\geq 0\), and \(g(s)>0\) for \(s>0\). The existence of at least one positive solution is obtained. The asymptotic behavior of positive solutions is also studied.