Infinitely many radial solutions of a mean curvature equation in Lorentz-Minkowski space

In this paper, we show that the quasilinear equation has a positive smooth radial solution at least for any α > 2* = 2N/(N- 2), N ≥ 3. Our approach is based on the study of the optimizers for the best constant in the inequality, which holds true in the unit ball of W1,1(ℝN)\D1;2(ℝN) if and only if and α2*. We also prove that the best constant is not achieved for α = 2*. As a byproduct, our arguments combined with Lusternik-Schnirelmann category theory allow to construct a sequence of radial solutions.La pagination indiquée dans la zone "Pages" est celle du tiré à part, numérisé par les Bibliothèques de l'ULB. La pagination, telle qu'elle apparait dans la revue, est pp. 259-284