Schrödinger-Maxwell equations driven by mixed local-nonlocal operators
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913334889021440 |
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| author | Cangiotti, Nicolò Caponi, Maicol Maione, Alberto Vitillaro, Enzo |
| author_facet | Cangiotti, Nicolò Caponi, Maicol Maione, Alberto Vitillaro, Enzo |
| contents | In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schrödinger-Maxwell equations and Schrödinger-Maxwell equations with a coercive potential, and the main novelty is that the nonlocal part of the operator is allowed to be nonpositive definite according to a real parameter. We then provide a range of parameter values to ensure the existence of solitary standing waves, obtained as Mountain Pass critical points for the associated energy functionals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_15655 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Schrödinger-Maxwell equations driven by mixed local-nonlocal operators Cangiotti, Nicolò Caponi, Maicol Maione, Alberto Vitillaro, Enzo Analysis of PDEs Mathematical Physics 35A01, 35A15, 35J50, 35J60, 35Q60, 35R11, 58E40 In this paper we prove existence of solutions to Schrödinger-Maxwell type systems involving mixed local-nonlocal operators. Two different models are considered: classical Schrödinger-Maxwell equations and Schrödinger-Maxwell equations with a coercive potential, and the main novelty is that the nonlocal part of the operator is allowed to be nonpositive definite according to a real parameter. We then provide a range of parameter values to ensure the existence of solitary standing waves, obtained as Mountain Pass critical points for the associated energy functionals. |
| title | Schrödinger-Maxwell equations driven by mixed local-nonlocal operators |
| topic | Analysis of PDEs Mathematical Physics 35A01, 35A15, 35J50, 35J60, 35Q60, 35R11, 58E40 |
| url | https://arxiv.org/abs/2307.15655 |