3 problems

Critical-curve conjecture. Based on the work of Kubo–Kubota–Sunagawa, the critical curve for system (2) is

Let $\Omega\subset\mathbb{R}^N$ be the domain in the Lane–Emden problem … with $1<p<2^*-1$, where $2^*$ is the critical Sobolev exponent. Assume that $\Omega$ is convex. Convex-dom…

Multi-dimensional controllability conjecture. Theorem remains true in this context if the growth condition on $g$ is strengthened to