4 problems

Let $n\geqslant 3$ and $\alpha\in(0,n)$. Consider a singular positive solution $u\in \mathcal{C}^{2}(\mathbb R^n\setminus\{0\})\cap L^{2^{*}_{\alpha}}(\mathbb{R}^{n})$ of the local…

Complete classification conjecture. Either $u\equiv 0$, or there exist $\lambda:=u(0)^{\frac{p}{N-p}}>0$ and $x_{0}\in\mathbb{R}^{N}$ such that

Let $u$ be a stable blow-up solution of the $L^2$-critical generalized Hartree equation, with blow-up time $T$, spatial dimension $d$, scale $L(t)$, center $x(t)$, phase parameter…

Chadam–Glassey conjecture. The equation with Yukawa potential $V$ can be derived by uncoupling the Dirac–Klein–Gordon equations.