3 problems

Strictness characterization.

Let $d=1$ and $s\in(0,\frac{1}{2})$. For $f\in\dot{H}^s(\mathbb{R})\setminus\mathcal B$, let $\mathcal Q(f)$ denote the Bianchi–Egnell quotient, let $c_{BE}(s)$ be its infimum, let…

Let $\Lambda^*<\lambda_*<\Lambda_1$ and set $\beta_*=1$. Let $S_{1,\lambda,\beta}$ denote the class of radial sign-changing solutions with the index specified in the paper, and let…