The Lane-Emden Equation revisited

Rafael Benguria P. Universidad Católica de Chile

Several results concerning existence and nonexistence of radial (but not necessarily positive) solutions to the nonlinear boundary value problem

−Δu = λu + |u|^{p−1}u,

on a (geodesic) ball of R^{N} or S^{3}, with Dirichlet boundary condition will be presented. In particular, a whole classification of radial solutions in the Euclidean case will be presented (depending on the possible values of λ and the exponent p). The dependence on the underlying space will be illustrated through a discussion of the BVP on S^{3}.

Supported by FONDECYT (Chile) 199-0427.