Please use this identifier to cite or link to this item:
http://hdl.handle.net/1843/34971
Type: | Tese |
Title: | Some results on a pseudo-relativistic Hartree equation and on a magnetic Choquard equation |
Authors: | Guido Gutierrez Mamani |
First Advisor: | Hamilton Prado Bueno |
First Co-advisor: | Gilberto de Assis Pereira |
First Referee: | Aldo Henrique de Souza Medeiros |
Second Referee: | Fábio Rodrigues Pereira |
Abstract: | In the first part of this work, we consider the asymptotically linear, strongly coupled nonlinear system By applying the Nehari-Pohozaev manifold, we prove that our system has a ground state solution. We also prove that solutions of this system are radially symmetric and belong to C^(0,μ) ( R N ) for some 0 < μ < 1 and each N > 1. In the final part of the work, we consider the stationary magnetic nonlinear Choquard equation −(∇ + iA ( x ))^(1/2) u + V ( x ) u =(1/|x|^(\alpha)∗ F (| u |))f (| u |) u/|u|. where A : R N → R N is a vector potential, V is a scalar potential, f : R → R and F is the primitive of f . Under mild hypotheses, we prove the existence of a ground state solution for this problem. We also prove a simple multiplicity result by applying Ljusternik–Schnirelmann methods. |
Subject: | Matemática – Teses Equações diferenciais parciais – Teses Princípios variacionais – Teses |
language: | eng |
metadata.dc.publisher.country: | Brasil |
Publisher: | Universidade Federal de Minas Gerais |
Publisher Initials: | UFMG |
metadata.dc.publisher.department: | ICEX - INSTITUTO DE CIÊNCIAS EXATAS |
metadata.dc.publisher.program: | Programa de Pós-Graduação em Matemática |
Rights: | Acesso Restrito |
URI: | http://hdl.handle.net/1843/34971 |
Issue Date: | 3-Nov-2020 |
metadata.dc.description.embargo: | 3-Nov-2021 |
Appears in Collections: | Teses de Doutorado |
Files in This Item:
File | Description | Size | Format | |
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TESE-GUIDO (1).pdf | 2 MB | Adobe PDF | View/Open |
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