7 problems

Low-index nonexistence conjecture. There are no solutions of $\mathrm{HSE}$ satisfying $\mathrm{HBC1}$--$\mathrm{HBC2}$ when $\nu(n,\sigma)\leq2$.

A distinct covering system is a covering system whose moduli are distinct integers greater than $1$. Let $m$ be its least modulus and let $L$ be the least common multiple of its mo…

Let $\phi$ solve the three-dimensional energy-critical wave equation and satisfy the no-outgoing-radiation condition, and consider multi-solitons whose ground-state components are…

Nonexistence conjecture. For subcritical exponents, positive classical solutions do not exist.

The low-dispersion nonexistence conjecture asserts that the profile equation has only the trivial solution in $H^{1/2}(\mathbb{R}^n)$, namely $Q\equiv0$. The conjecture concerns th…

Let $\alpha\in(0,n)$, let $p,q$ be positive exponents, and consider the Hardy–Littlewood–Sobolev system … Define the critical Sobolev hyperbola by…

Subcritical nonexistence conjecture. The system has no positive solution whenever