On positive solutions of \(\Delta{} u +\lambda{} f (u)=0\) with \(f\) discontinuous (Q1177008)

In this paper the authors discuss the existence of radially symmetric solutions of the Dirichlet problem for \(-\Delta u=\lambda f(u)\) on the unit ball in \(R^ n\) when \(f\) has a jump discontinuity at \(u=1\). They assume that there is a branch \((u_ \gamma, \lambda(\gamma))\) of solutions (where \(\sup u_ \gamma=\gamma\)) defined for \(\gamma<1\) and consider the extension of the branch across \(\gamma=1\). They also consider the stability of these solutions (for an appropriate porous medium type parabolic operator).