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^ \...

Descripción completa

Detalles Bibliográficos
Autor: Mascaro, Bruno
Tipo de recurso: tesis doctoral
Estado:Versión publicada
Fecha de publicación:2022
País:Brasil
Institución: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
Acceso en línea:https://www.teses.usp.br/teses/disponiveis/45/45131/tde-07032023-211714/
Access Level:acceso abierto
Palabra clave:Ljusternik-Schnirelmann
Schrödinger-Bopp-Podolsky
Sistema de equações diferenciais parciais
Descripción
Sumario: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.