Lack of uniqueness for an elliptic equation with nonlinear and nonlocal drift posed on a torus
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866911417760743424 |
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| author | Muntean, Adrian Rui, Giulia |
| author_facet | Muntean, Adrian Rui, Giulia |
| contents | We study a nonlinear and nonlocal elliptic equation posed on the flat torus. While constant solutions always exist, we show that uniqueness fails in general. Using spectral analysis and the Crandall--Rabinowitz bifurcation theorem, we prove the existence of branches of non-constant periodic solutions bifurcating from constant states. This result is qualitative and non-constructive. Using a conceptually different argument, we construct explicit multiple solutions for a specific one--dimensional formulation of our target problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02818 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Lack of uniqueness for an elliptic equation with nonlinear and nonlocal drift posed on a torus Muntean, Adrian Rui, Giulia Analysis of PDEs 35J60, 35A02, 35B10, 35B32 We study a nonlinear and nonlocal elliptic equation posed on the flat torus. While constant solutions always exist, we show that uniqueness fails in general. Using spectral analysis and the Crandall--Rabinowitz bifurcation theorem, we prove the existence of branches of non-constant periodic solutions bifurcating from constant states. This result is qualitative and non-constructive. Using a conceptually different argument, we construct explicit multiple solutions for a specific one--dimensional formulation of our target problem. |
| title | Lack of uniqueness for an elliptic equation with nonlinear and nonlocal drift posed on a torus |
| topic | Analysis of PDEs 35J60, 35A02, 35B10, 35B32 |
| url | https://arxiv.org/abs/2602.02818 |