On the fourth-order Joseph-Lundgren exponent

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

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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.

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Received: June 2017
Published online: August 2017

Authors:

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

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