Banca de DEFESA: Thafne Sirqueira Carvalho

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : Thafne Sirqueira Carvalho
DATE: 12/07/2024
TIME: 11:00
LOCAL: auditório do MAT
TITLE:

Semilinear equations with potential that change sign with negative and positive spectrum

KEY WORDS:

Mountain Pass Geometry, Cerami Sequence, Linking, Nehari Variety.

PAGES: 102
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

$$-\Delta u+V(x)u=f(u) \ \ \textrm{in} \ \ \mathbb{R}^N \eqno{(P)}$$
with $u \in H^1(\mathbb{R}^N)\backslash \{0\}$ where $N \geq 3$ and $V$ is a potential that changes sign and has a positive limit at infinity. First, we obtain a minimum energy positive solution and a nodal solution to the problem $(P)$, with V satisfying defined conditions and $f$ being a superlinear function with subcritical growth. The existence of this solution was guaranteed using variational techniques combined with the Lions Principle of Concentration and Compactness. Furthermore, through the Nehari manifold we ensure that the functional associated with the problem has the Mountain Pass Geometry.

COMMITTEE MEMBERS:
Presidente - 2570378 - RICARDO RUVIARO
Interno - 1177944 - GIOVANY DE JESUS MALCHER FIGUEIREDO
Interno - 2307366 - MARCELO FERNANDES FURTADO
Externo à Instituição - JOSÉ CARLOS DE OLIVEIRA JUNIOR - UFNT