par Bonheure, Denis 
;De Coster, C;Derlet, Ann
Référence Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, 44, 1, page (1-26)
Publication Publié, 2012
;De Coster, C;Derlet, Ann Référence Rendiconti dell'Istituto di Matematica dell'Universita di Trieste, 44, 1, page (1-26)
Publication Publié, 2012
Article révisé par les pairs
| Résumé : | 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. |
