Positivity of nonnegative solutions for cooperative semipositone systems. (Q2784676)

This paper deals with a classical nonnegative solution \((u\geq 0\), \(v\geq 0)\) for the system NEWLINE\[NEWLINE\begin{aligned} -\Delta u= f(v)&\quad\text{in }\Omega,\\ -\Delta v= g(u)&\quad\text{in }\Omega,\tag{1}\\ u= 0= v&\quad\text{on }\partial\Omega,\end{aligned}NEWLINE\]NEWLINE where \(\Omega\) is a ball in \(\mathbb{R}^n\) for \(n> 1\), \(\partial\Omega\) its boundary and \(f,g: [0,\infty)\to \mathbb{R}\) are \(C^1\) functions satisfying \(f(0)> 0\) and \(g(0)> 0\) and \(f'\geq 0\) and \(g'\geq 0\). The authors show that nonnegative solutions for (1) in a ball are positive and as a result radially symmetric.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00016].