The polyharmonic Hénon--Lane--Emden conjecture

Phuong Le

We study positive classical solutions of the polyharmonic Hénon--Lane--Emden system $(-\Delta {)}^{m}u=|x{|}^{\alpha }{v}^p$, $(-\Delta {)}^{m}v=|x{|}^{\beta }{u}^q$ in ${\mathbb{R}}^n$, where $m\ge 2$, $p,q\ge 1$, $pq>1$, an…