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