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

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dc.creatorGuido Gutierrez Mamani
dc.date.accessioned2021-02-09T19:03:04Z
dc.date.accessioned2025-09-08T23:30:20Z
dc.date.issued2020-11-03
dc.description.sponsorshipCAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
dc.identifier.urihttps://hdl.handle.net/1843/34971
dc.languageeng
dc.publisherUniversidade Federal de Minas Gerais
dc.rightsAcesso Restrito
dc.subjectMatemática – Teses
dc.subjectEquações diferenciais parciais – Teses
dc.subjectPrincípios variacionais – Teses
dc.subject.otherPohozaev Identity
dc.subject.otherFractional laplacian
dc.subject.otherChoquard equation
dc.subject.otherSplitting lemma
dc.titleSome results on a pseudo-relativistic Hartree equation and on a magnetic Choquard equation
dc.typeTese de doutorado
local.contributor.advisor-co1Gilberto de Assis Pereira
local.contributor.advisor1Hamilton Prado Bueno
local.contributor.advisor1Latteshttp://lattes.cnpq.br/0867903003222790
local.contributor.referee1Aldo Henrique de Souza Medeiros
local.contributor.referee1Fábio Rodrigues Pereira
local.creator.Latteshttp://lattes.cnpq.br/3828899577351511
local.description.embargo2021-11-03
local.description.resumoIn 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.
local.publisher.countryBrasil
local.publisher.departmentICEX - INSTITUTO DE CIÊNCIAS EXATAS
local.publisher.initialsUFMG
local.publisher.programPrograma de Pós-Graduação em Matemática

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