Spectral and related properties about the Emden-Fowler equation \(-\Delta u=\lambda e^ u\) on circular domains (Q1327091)

The Emden-Fowler equation with Dirichlet boundary conditions is investigated. The domain is assumed to be the unit ball or an annulus in \(\mathbb{R}^ n\) with \(2<n<10\). The authors study the behaviour of radially symmetric solutions for varying values of \(\lambda\) and the annulus' inner radius. The linearized problem in radial direction is solved using the Emden transformation yielding an autonomous nonlinear ordinary differential equation, which can be investigated by phase plane analysis. Also the occurrence of nonradial bifurcations in the annular case is treated.