A note on the nonlinear Schrödinger equation in a general domain
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2017
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| _version_ | 1866912245824356352 |
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| author | Hayashi, Masayuki |
| author_facet | Hayashi, Masayuki |
| contents | We consider the Cauchy problem for nonlinear Schrödinger equations in a general domain $Ω\subset\mathbb{R}^N$. Construction of solutions has been only done by classical compactness method in previous results. Here, we construct solutions by a simple alternative approach. More precisely, solutions are constructed by proving that approximate solutions form a Cauchy sequence in some Banach space. We discuss three different types of nonlinearities: power type nonlinearities, logarithmic nonlinearities and damping nonlinearities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1712_10239 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | A note on the nonlinear Schrödinger equation in a general domain Hayashi, Masayuki Analysis of PDEs We consider the Cauchy problem for nonlinear Schrödinger equations in a general domain $Ω\subset\mathbb{R}^N$. Construction of solutions has been only done by classical compactness method in previous results. Here, we construct solutions by a simple alternative approach. More precisely, solutions are constructed by proving that approximate solutions form a Cauchy sequence in some Banach space. We discuss three different types of nonlinearities: power type nonlinearities, logarithmic nonlinearities and damping nonlinearities. |
| title | A note on the nonlinear Schrödinger equation in a general domain |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1712.10239 |