6 problems

For a global curve of rotating vortex-pair solutions, with the vortices either corotating or counter-rotating, the limiting configuration is expected to consist of vortex patches i…

The global bifurcation argument uses the Dubreil-Jacotin formulation for elevation bores, which rules out stagnation points and allows the interface to be shown not to meet the wal…

Consider positive solutions of … under the condition $f_r(r,u)\leq 0$. In dimension $n=1$, the value $u(0)$ is known to be a global parameter. Global-parameter conjecture. The same…

Let $(x_*,0,\lambda_*)$ be a simple solution of the eigenvalue problem, meaning that the first three hypotheses stated in the paper hold. Suppose that $G$ and $H$ are separable, an…

Let $L\colon\mathbb{R}^k\to\mathbb{R}^k$ be a linear operator, let $\mathbf{S}$ be the unit sphere in $\mathbb{R}^k$, and let $N\colon\mathbf{S}\to\mathbb{R}^k$ be continuous. For…

Let ${\mathcal K}$ be the global curve of steady gravity water waves, and let its furthest boundary refer to the boundary described in the surrounding global-bifurcation analysis.…