Some results on a pseudo-relativistic Hartree equation and on a magnetic Choquard equation

Guido Gutierrez Mamani

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

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