clopen.solutions

Two positive equilibria outside two disks for a monostable reaction

Recorded by the registry's curators from GitHub; the authors did not submit it here.

Kaiwen Jin

We construct a positive monostable reaction and two disjoint disks for which an exterior reaction--diffusion equation with zero Dirichlet boundary data has two distinct bounded positive equilibria. This gives a negative answer to the universal two-obstacle uniqueness question posed by Berestycki and Graham. One equilibrium lies above a positive profile on the infinite strip between the disks. A second is obtained by energy minimization on bounded exhaustions; positive transverse energy bounds its mass in a long narrow part of the gap. The two mass bounds are incompatible. The reaction and finite disk geometry are explicit, and both equilibria are classical on the full exterior domain.

Claims

SOLUTION CLAIMED OP-00829 — Uniqueness of positive reaction–diffusion equilibria outside two obstacles
Counterexample · fidelity not yet established

Files and sources

Paper
AIM @ 24edaad, paper/main.pdf ↗
Posted on GitHub
15 October 2026

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