Singular solutions of semilinear elliptic equations with exponential nonlinearities in 2-dimensions
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917626911916032 |
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| author | Fujishima, Yohei Ioku, Norisuke Ruf, Bernhard Terraneo, Elide |
| author_facet | Fujishima, Yohei Ioku, Norisuke Ruf, Bernhard Terraneo, Elide |
| contents | By introducing a new classification of the growth rate of exponential functions, singular solutions for semilinear elliptic equations in 2-dimensions with exponential nonlinearities are constructed. The strategy is to introduce a model nonlinearity which admits an explicit singular solution. Then, using a transformation as in [8], one obtains an approximate singular solution, and then one concludes by a suitable fixed point argument. Our method covers a wide class of nonlinearities in a unified way. As a special case, our result contains a pioneering contribution by Ibrahim--Kikuchi--Nakanishi--Wei [15] for the Moser--Trudinger type nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00258 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular solutions of semilinear elliptic equations with exponential nonlinearities in 2-dimensions Fujishima, Yohei Ioku, Norisuke Ruf, Bernhard Terraneo, Elide Analysis of PDEs 35J61, 35B40, 35A24 By introducing a new classification of the growth rate of exponential functions, singular solutions for semilinear elliptic equations in 2-dimensions with exponential nonlinearities are constructed. The strategy is to introduce a model nonlinearity which admits an explicit singular solution. Then, using a transformation as in [8], one obtains an approximate singular solution, and then one concludes by a suitable fixed point argument. Our method covers a wide class of nonlinearities in a unified way. As a special case, our result contains a pioneering contribution by Ibrahim--Kikuchi--Nakanishi--Wei [15] for the Moser--Trudinger type nonlinearity. |
| title | Singular solutions of semilinear elliptic equations with exponential nonlinearities in 2-dimensions |
| topic | Analysis of PDEs 35J61, 35B40, 35A24 |
| url | https://arxiv.org/abs/2404.00258 |