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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2404.05066 |
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| _version_ | 1866916197477384192 |
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| author | Kolonitskii, S. B. Lerman, L. M. Nazarov, A. I. |
| author_facet | Kolonitskii, S. B. Lerman, L. M. Nazarov, A. I. |
| contents | We study the stationary Swift--Hohenberg equation $(Δ+ 1)^2 u - αu - βu^2 + u^3=0$ in the whole space $\mathbb R^n$, $2\le n \le 7$. We develop and modify the variational approach introduced by Lerman, Naryshkin and Nazarov (2020) and obtain a series of periodic solutions with certain additional symmetries. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Entire solutions to the Swift--Hohenberg equation via variational approach Kolonitskii, S. B. Lerman, L. M. Nazarov, A. I. Analysis of PDEs 35J35, 35B06, 35B45 We study the stationary Swift--Hohenberg equation $(Δ+ 1)^2 u - αu - βu^2 + u^3=0$ in the whole space $\mathbb R^n$, $2\le n \le 7$. We develop and modify the variational approach introduced by Lerman, Naryshkin and Nazarov (2020) and obtain a series of periodic solutions with certain additional symmetries. |
| title | Entire solutions to the Swift--Hohenberg equation via variational approach |
| topic | Analysis of PDEs 35J35, 35B06, 35B45 |
| url | https://arxiv.org/abs/2404.05066 |