4 problems

Let $(V,\b5)$ be a weighted graph, let $o\in V$, and let $\sigma>1$. A nonnegative solution $u$ of the elliptic inequality … is a function on $V$ satisfying this inequality, where…

Let $F$ denote the dimensionless wave speed, or Froude number, of a solitary water wave, with $F>1$ meaning that the wave is supercritical. Craig–Sternberg's conjecture. All solita…

Let $1<p<N-1$, let $q_c$ be the critical exponent defined in the paper, and let $S\subset S^{N-1}_+$ be star-shaped. Consider the boundary-value problem … is that this problem admi…

Strict copositivity conjecture. Strict copositivity of $B$ should be sufficient to ensure that the system admits no nontrivial solution.