On the global bifurcation diagram of the equation $-Δu=μ|x|^{2α}e^u$ in dimension two
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866914805431926784 |
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| author | Bartolucci, Daniele Jevnikar, Aleks Wu, Ruijun |
| author_facet | Bartolucci, Daniele Jevnikar, Aleks Wu, Ruijun |
| contents | The aim of this note is to present the first qualitative global bifurcation diagram of the equation $-Δu=μ|x|^{2α}e^u$. To this end, we introduce the notion of domains of first/second kind for singular mean field equations and base our approach on a suitable spectral analysis. In particular, we treat also non-radial solutions and non-symmetric domains and show that the shape of the branch of solutions still resembles the well-known one of the model regular radial case on the disk. Some work is devoted also to the asymptotic profile for $μ\to-\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16990 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the global bifurcation diagram of the equation $-Δu=μ|x|^{2α}e^u$ in dimension two Bartolucci, Daniele Jevnikar, Aleks Wu, Ruijun Analysis of PDEs 35B45, 35J60, 35J99 The aim of this note is to present the first qualitative global bifurcation diagram of the equation $-Δu=μ|x|^{2α}e^u$. To this end, we introduce the notion of domains of first/second kind for singular mean field equations and base our approach on a suitable spectral analysis. In particular, we treat also non-radial solutions and non-symmetric domains and show that the shape of the branch of solutions still resembles the well-known one of the model regular radial case on the disk. Some work is devoted also to the asymptotic profile for $μ\to-\infty$. |
| title | On the global bifurcation diagram of the equation $-Δu=μ|x|^{2α}e^u$ in dimension two |
| topic | Analysis of PDEs 35B45, 35J60, 35J99 |
| url | https://arxiv.org/abs/2306.16990 |