4 problems

Endpoint behavior conjecture. There exists $E_k>0$ such that if

Let $m,n$ be the mode indices, let $P$ be the parameter, and define … Let $\Theta_m$ and $\Theta_n$ be the corresponding modes with energy $E_{\Theta_m}$. Assume … Let $E_1$ and…

Let $m,n$ be the mode indices, let $P$ be the parameter, and let $\Theta_m$ and $\Theta_n$ denote the corresponding modes with energy $E_{\Theta_m}$. Assume … Let $E_2$ be the thre…

All-energy stability conjecture. Under these assumptions, $\Theta_m$ is linearly stable with respect to $\Theta_n$ for every $E_{\Theta_m}>0$.