• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2020.tde-22042020-123659
Document
Author
Full name
Danilo Gregorin Afonso
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2020
Supervisor
Committee
Siciliano, Gaetano (President)
Laurain, Antoine
Paiva, Francisco Odair Vieira de
Title in English
Normalized solutions for a Schrödinger-Bopp-Podolsky system
Keywords in English
Deformation lemma
Krasnoselskii genus
Lagrange multipliers
Schrödinger-Bopp-Podolsky system
weak solutions
Abstract in English
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.
Title in Portuguese
Soluções normalizadas para um sistema de Schrödinger-Bopp-Podolsky
Keywords in Portuguese
Gênero de Krasnoselskii
Lema de deformação
Multiplicadores de Lagrange
Sistema de Schrödinger-Bopp-Podolsky
Soluções fracas
Abstract in Portuguese
Objetivamos estudar um sistema de tipo Schrödinger-Bopp-Podolsky, que consiste de duas equações diferenciais parciais não lineares. Apresentamos um resultado original de existência e multiplicidade de soluções fracas para o problema, ou seja, de existência de pontos críticos de um funcional restrito a uma subvariedade de um espaço de Hilbert. É desenvoldida a teoria do cálculo em espaços de Banach. Discutimos a teoria do gênero de Krasnoselskii e apresentamos o Lema de Deformação e noções correlatas. Discutimos subvariedades em um espaço de Banach e multiplicadores de Lagrange. Provamos a existência e multiplicidade de soluções fracas para o problema proposto.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
Versao_submetida.pdf (699.39 Kbytes)
Publishing Date
2020-04-28
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
CeTI-SC/STI
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2020. All rights reserved.