A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915423894634496 |
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| author | Bartolucci, Daniele Hu, Yeyao Jevnikar, Aleks Wei, Juncheng Yang, Wen |
| author_facet | Bartolucci, Daniele Hu, Yeyao Jevnikar, Aleks Wei, Juncheng Yang, Wen |
| contents | We consider a Hamiltonian system of free boundary type, showing first uniform bounds and existence of solutions and of the free boundary. Then, for any smooth and bounded domain, we prove uniqueness of positive solutions in a suitable interval and show that the associated energies and boundary values have a monotonic behavior. Some consequences are discussed about the parametrization of the unbounded Rabinowitz continuum for a class of superlinear strongly coupled elliptic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01849 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions Bartolucci, Daniele Hu, Yeyao Jevnikar, Aleks Wei, Juncheng Yang, Wen Analysis of PDEs 35J57, 35B30, 35B32, 35R35 We consider a Hamiltonian system of free boundary type, showing first uniform bounds and existence of solutions and of the free boundary. Then, for any smooth and bounded domain, we prove uniqueness of positive solutions in a suitable interval and show that the associated energies and boundary values have a monotonic behavior. Some consequences are discussed about the parametrization of the unbounded Rabinowitz continuum for a class of superlinear strongly coupled elliptic systems. |
| title | A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions |
| topic | Analysis of PDEs 35J57, 35B30, 35B32, 35R35 |
| url | https://arxiv.org/abs/2508.01849 |