Normalized solutions for a Schrödinger-Bopp-Podolsky system

• Ano de defesa: 2020
• Autor(a) principal: Afonso, Danilo Gregorin
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Deformation lemma; Gênero de Krasnoselskii; Krasnoselskii genus; Lagrange multipliers; Lema de deformação; Multiplicadores de Lagrange; Schrödinger-Bopp-Podolsky system; Sistema de Schrödinger-Bopp-Podolsky; Soluções fracas; weak solutions
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/45/45131/tde-22042020-123659/

The aim is to study a Schrödinger-Bopp-Podolsky system of partial differential equations. We present an original result for the existence and multiplicity of weak solutions to the problem, which consists in the determination of critical points for a functional constrained to a submanifold of a Hilbert space. The calculus in Banach spaces is developed. Krasnoselskii\'s genus theory is discussed, after which the Deformation Lemma and some related notions are presented. Submanifolds of Banach spaces and Lagrange multipliers are discussed. The existence and multiplicity of solutions to the proposed problem is proved.