Nonlinear scalar field equation with point interaction
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909782452994048 |
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| author | Pomponio, Alessio Watanabe, Tatsuya |
| author_facet | Pomponio, Alessio Watanabe, Tatsuya |
| contents | This paper is devoted to the study of the nonlinear scalar field equation with a point interaction at the origin in dimensions two and three. By applying the mountain pass theorem and the technique of adding one dimensional space, we prove the existence of a nontrivial singular solution for a wide class of nonlinearities. We also establish the Pohozaev identity by proving a pointwise estimate of the gradient near the origin. Some qualitative properties of nontrivial solutions are also given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00189 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Nonlinear scalar field equation with point interaction Pomponio, Alessio Watanabe, Tatsuya Analysis of PDEs 35J20, 35Q55 This paper is devoted to the study of the nonlinear scalar field equation with a point interaction at the origin in dimensions two and three. By applying the mountain pass theorem and the technique of adding one dimensional space, we prove the existence of a nontrivial singular solution for a wide class of nonlinearities. We also establish the Pohozaev identity by proving a pointwise estimate of the gradient near the origin. Some qualitative properties of nontrivial solutions are also given. |
| title | Nonlinear scalar field equation with point interaction |
| topic | Analysis of PDEs 35J20, 35Q55 |
| url | https://arxiv.org/abs/2410.00189 |