5 problems

Consider the nonlocal two-component Bose–Einstein system involving the fractional Laplacian $(-\Delta)^s$, with exponent $s>0$, in Euclidean space $\mathbb{R}^{n}$. De Giorgi prope…

The paper considers the more general problems referred to as … , in the one-dimensional case $N=1$. Conjecture. A similar strategy to the one used for the ball case with $N=1$ and…

Let $\{X_n\}_n$ and $\{Y_n\}_n$ be matrix-sequences with $X_n,Y_n\in\mathbb C^{d_n\times d_n}$. Assume that $X_n$ is Hermitian for all $n$ and $\{X_n\}_n\sim_{\lambda}f$, where $f$…

Uniqueness hypothesis conjecture. The hypothesis $$ should be valid for all $cfrac{1}{2}$.

The paper considers the fractional elliptic problem … with $s\in(\frac{1}{2},1)$, nondecreasing $f\in C(\mathbb R)$ satisfying $t f(t)\geq 0$, and data $\tau\in L^1(\Omega,\rho^s)$…