3 problems

Extremal-parameter conjecture. For the problem $Q_{\lambda}$, the extremal parameter is

Extremal-parameter conjecture. The extreme value for $P_{\lambda}$ is

Let $\sigma$ lie in the $L^2$-supercritical and $H^2$-subcritical regime, namely … Consider the radial nonlinear eigenvalue problem for $\tilde S_{\mathrm B}(\rho)$ with $\nu=1$: ……