4 problems

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Conjecture on the maximal-time dichotomy for the nonlinear Sobolev system
Maximal-time dichotomy conjecture.
Conjectureopennonlinear-odes sobolev-embeddingsarXiv posted 2 days ago
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Conjecture on non-oscillatory behavior of solutions near the maximal time
Non-oscillation conjecture. The same conclusion holds for all $p>1$ and $q>1$ .
Conjectureopennonlinear-odes oscillation-theory sobolev-embeddingsarXiv posted 2 days ago
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Persistence conjecture for the Hastings–McLeod solution under Thomas–Fermi perturbations
Let $u0$ be the Hastings–McLeod solution of the Painlevé-II equation … with the asymptotic behavior specified by the Painlevé-II boundary conditions. For $q>\frac{5}{6}$ , consider…
Conjecturesolvedasymptotic-analysis nonlinear-odes painleve-equationsarXiv posted 2 days ago
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Uniqueness of the bounded solution under a quadratic bound on the heat-flux function
Uniqueness conjecture. The boundary value problem has a unique bounded solution.
Conjectureopenboundary-value-problems free-convection nonlinear-odesarXiv posted 2 days ago

Conjecture on the maximal-time dichotomy for the nonlinear Sobolev system