2 problems

Let $B$ be the unit ball of $\mathbb{R}^n$, and let $k\in\mathbb{N}$ satisfy $n>2k\geq 2$. Consider $\lambda\in\mathbb{R}$ and $u\in C^{2k}(\overline{B})$ solving … where…

Hé non-Lane-Emden conjecture. If $(u,v)$ is a nonnegative solution of the system and $(p,q)$ is under the critical hyperbola, then $u=v=0$. This is a Liouville-type conjecture for…