Some results on a pseudo-relativistic Hartree equation and on a magnetic Choquard equation
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Universidade Federal de Minas Gerais
Descrição
Tipo
Tese de doutorado
Título alternativo
Primeiro orientador
Membros da banca
Aldo Henrique de Souza Medeiros
Fábio Rodrigues Pereira
Fábio Rodrigues Pereira
Resumo
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.
Abstract
Assunto
Matemática – Teses, Equações diferenciais parciais – Teses, Princípios variacionais – Teses
Palavras-chave
Pohozaev Identity, Fractional laplacian, Choquard equation, Splitting lemma