A dynamical system approach to the Chandrasekhar-Hamilton-Jacobi equation

Abstract

48 pagesInternational audienceWe study the local properties of positive solutions of the equation -∆u = e^u -M |∇u|^q in a punctured domain Ω \ {0} of R^N in the range of parameters q> 1 and M>0. We prove a series of a priori estimates near a singular point. In the case of radial solutions we use various techniques inherited from the dynamical systems theory to obtain the precise behaviour of singular solutions. We prove also the existence of singular solutions with these precise behaviours