Schrödinger-Bopp-Podolsky system in R³

• Autor(a) principal: Mascaro, Bruno
• Data de Publicação: 2022
• Tipo de documento: Tese
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-07032023-211714/
• topic: Ljusternik-Schnirelmann; Schrödinger-Bopp-Podolsky; Sistema de equações diferenciais parciais

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.