# 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