6 problems

Let $u_\alpha$ and $u_\beta$ be the corresponding solutions of the fractional parabolic equation … with $0<\beta<\alpha<1$ and non-negative, even, unimodal initial data as specifie…

Fractional Lane–Emden conjecture. If

Let $u\in C^2(\mathbb{R}^{n})$ satisfy $|u|<1$ and be a stable critical point of $E_{s,\varepsilon}$. Stability conjecture. If $n\leq7$, then $u$ is one-dimensional provided…

Let $\psi_0$ be the even, single-lobe periodic wave from the even periodic-wave theorem, write … and define $\omega_0=c_0-6a_0^2$. Let $\phi(\cdot,\omega,a)$ be the associated loca…

Let $\alpha \in \left(\frac{1}{2},2\right]$ and $c \in (-1,\infty)$. Let $\psi$ be the odd, single-lobe periodic wave obtained as in the odd periodic-wave theorem, and let…

Let $\widetilde{\mathbb M}$ and $\widetilde{\mathbb S}$ denote the finite element mass and stiffness matrices, respectively, and let $\widetilde{\mathbb A}^{\alpha}$ be the discret…