On the fourth-order Joseph-Lundgren exponent

On the fourth-order Joseph-Lundgren exponent

Abdellaziz Harrabi and Belgacem Rahal – GJM, Volume 2, Issue 1 (2017), 37-41.

In this paper, we revise the proof of the existence and the explicit value of the fourth-order Joseph–Lundgren exponent p_c(n,4) computed by Gazzola and Grunau [FH] (see also [10], [5]). Inspired by our work in [13], we propose a simple proof based on a symmetry property that allows us to reduce the computation of p_c(n,4) into solving a second degree polynomial equation. Therefore we can easily derive the explicit value of this exponent. Our approach is much more streamlined and more transparent compared to [9],[10] in terms of finding this explicit value.

Categories: Issue1, 2017


Received: June 2017
Published online: August 2017


Abdellaziz Harrabi
Institut Supérieur des Mathématiques Appliquées et de l'Informatique,
Université de Kairouan, Tunisia
Belgacem Rahal
Faculté des Sciences, Département de Mathématiques,
B.P 1171 Sfax 3000, Université de Sfax, Tunisia