Banca de DEFESA: LARYSSA KELY ALVES RODRIGUES

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : LARYSSA KELY ALVES RODRIGUES
DATE: 21/11/2025
TIME: 10:00
LOCAL: Auditório da UAMat
TITLE:

Existence of solutions with prescribed norm for a class of semilinear elliptic equations

KEY WORDS:

Normalized solutions; variational methods; nonlinear eigenvalue problem; minimax approach.

PAGES: 104
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUBÁREA: Análise
SPECIALTY: Equações Diferenciais Parciais
SUMMARY:

In this work, we intend to study the existence of normalized solutions for a class of semilinear elliptic equations of the type $-\Delta u=\lambda u +g(u)$ in $\mathbb{R}^N$, with certain conditions on the function $g$. In recent years, this type of problem has attracted great interest because the norm is preserved from evolution, being relevant for physics. We know that, in $\mathbb{R}^N$, we lose compactness in Sobolev embeddings. Thus, to circumvent this situation, Jeanjean (1997) worked in the space $H^1_{rad}(\mathbb{R}^N)$. Through a variational approach based on Ekeland's Variational Principle and the Mountain Pass, the author establishes the existence of solutions. In this sense, we will present in detail the results obtained by Jeanjean (1997), which is one of the first works to address this topic and widely referenced.

COMMITTEE MEMBERS:
Presidente - 1370096 - ROMILDO NASCIMENTO DE LIMA
Interno - 337123 - MARCO AURELIO SOARES SOUTO
Externo à Instituição - CÉSAR ENRIQUE TORRES LEDESMA - UNT