A remark on the critical explosion parameter for a semilinear elliptic equation in a generic domain using an explosion time of an ordinary differential equation

This paper gives a new criterion for estimating the critical explosion parameter of a semilinear elliptic equation with Dirichlet conditions on a bounded or unbounded domain, using simple evaluations of the geometric part of the problem on one hand, and of an explosion time for a first order ordinary differential equation on the other hand. This criterion is evaluated in the special case of a ball, and compared with other usual criteria deduced from the properties of the first eigenfunction of the laplacien, and from Pohozaev's method.