Schrödinger-Bopp-Podolsky system in R³
In this work we study the following perturbed Schrödinger-Bopp-Podolsky system in R³ \\begin\\label{eq:Pe}\\tag{$P_{\\varepsilon}$} \\left\\{ \\begin[c] -\\varepsilon^2\\Delta w +V(x)w + \\psi w = f(w) \\medskip \\\\ -\\varepsilon^2\\Delta \\psi + \\varepsilon^4\\Delta^\\psi = 4\\pi\\varepsilon w^ \...
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| Formato: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | Brasil |
| Recursos: | Universidade de São Paulo (USP) |
| Repositorio: | Biblioteca Digital de Teses e Dissertações da USP |
| Idioma: | inglés |
| OAI Identifier: | oai:teses.usp.br:tde-07032023-211714 |
| Acesso em linha: | https://www.teses.usp.br/teses/disponiveis/45/45131/tde-07032023-211714/ |
| Access Level: | acceso abierto |
| Palavra-chave: | Ljusternik-Schnirelmann Schrödinger-Bopp-Podolsky Sistema de equações diferenciais parciais |
| Resumo: | In this work we study the following perturbed Schrödinger-Bopp-Podolsky system in R³ \\begin\\label{eq:Pe}\\tag{$P_{\\varepsilon}$} \\left\\{ \\begin[c] -\\varepsilon^2\\Delta w +V(x)w + \\psi w = f(w) \\medskip \\\\ -\\varepsilon^2\\Delta \\psi + \\varepsilon^4\\Delta^\\psi = 4\\pi\\varepsilon w^ \\end ight. \\end and using variational methods and the Ljusternik-Schnirelmann theory, we show a lower bound for the number of solutions of such system. Along the work, some preliminaries notions are presented and the development of the system, together with brief historical notes about the physical framework of the problem. |
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