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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.12905 |
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| _version_ | 1866911007142576128 |
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| author | Ianni, Isabella Luo, Peng Yan, Shusen |
| author_facet | Ianni, Isabella Luo, Peng Yan, Shusen |
| contents | We consider multi-spike positive solutions to the Lane-Emden problem in any bounded smooth planar domain and compute their Morse index, extending to the dimension $N=2$ classical theorems due to Bahri-Li-Rey (1995) and Rey (1999) when $N\geq 4$ and $N=3$, respectively. Furthermore, by deeply investigating their concentration behavior, we also derive the total topological degree. The Morse index and the degree counting formula yield a new local uniqueness result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_12905 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Morse index, topological degree and local uniqueness of multi-spikes solutions to the Lane-Emden problem in dimension two Ianni, Isabella Luo, Peng Yan, Shusen Analysis of PDEs We consider multi-spike positive solutions to the Lane-Emden problem in any bounded smooth planar domain and compute their Morse index, extending to the dimension $N=2$ classical theorems due to Bahri-Li-Rey (1995) and Rey (1999) when $N\geq 4$ and $N=3$, respectively. Furthermore, by deeply investigating their concentration behavior, we also derive the total topological degree. The Morse index and the degree counting formula yield a new local uniqueness result. |
| title | Morse index, topological degree and local uniqueness of multi-spikes solutions to the Lane-Emden problem in dimension two |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.12905 |