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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2512.05743 |
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| _version_ | 1866912946863472640 |
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| author | Li, Yunxiao Zhang, Yanyan |
| author_facet | Li, Yunxiao Zhang, Yanyan |
| contents | This paper investigates an elliptic MEMS-Type equation with Henon and external pressure terms: Delta u = lambda|x|^alpha / u^p + F for x in R^N \ {0}, with u(0)=0 and u>0 for x in R^N \ {0}, where N >= 1, lambda > 0, p > 0, alpha > -2 and F in R are constants. We study positive rupture solutions with rupture point at the origin (u(0)=0). Our main emphasis is on asymptotic radial rupture solutions: we prove the existence of both radial and non-radial solutions, characterize their asymptotic behavior near the origin, and obtain a full asymptotic expansion of arbitrary order. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_05743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Asymptotic Behavior of Rupture Solutions for the Elliptic MEMS Equation with Hénon-Type and External Pressure Terms Li, Yunxiao Zhang, Yanyan Analysis of PDEs 35J75, 35J61, 35C20, 35B40, 74K15, 74G70 This paper investigates an elliptic MEMS-Type equation with Henon and external pressure terms: Delta u = lambda|x|^alpha / u^p + F for x in R^N \ {0}, with u(0)=0 and u>0 for x in R^N \ {0}, where N >= 1, lambda > 0, p > 0, alpha > -2 and F in R are constants. We study positive rupture solutions with rupture point at the origin (u(0)=0). Our main emphasis is on asymptotic radial rupture solutions: we prove the existence of both radial and non-radial solutions, characterize their asymptotic behavior near the origin, and obtain a full asymptotic expansion of arbitrary order. |
| title | Asymptotic Behavior of Rupture Solutions for the Elliptic MEMS Equation with Hénon-Type and External Pressure Terms |
| topic | Analysis of PDEs 35J75, 35J61, 35C20, 35B40, 74K15, 74G70 |
| url | https://arxiv.org/abs/2512.05743 |