A priori estimates and uniqueness of inflection points for positive solutions of semiposition problems (Q1343076)

The paper concerns the positive solutions to the system \(-\Delta u = \lambda f(u)\) in \(\Omega\), \(u = 0\) on \(\partial \Omega\). Here \(\Omega\) denotes the unit ball in \(R^ N\), centered at the origin and \(\lambda > 0\). These solutions are radially symmetric and strictly decreasing in \(r\) for \(r \in (0,1)\) where \(r = \| x \|\); under appropriate assumptions on \(f\), a priori estimates are established for \(\lambda f(u(0))/u (0)\). The results are related to the inflection points of \(u\).