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:
 In this work, we study the existence of a non-trivial solution to the nonlinear Schr\"odinger equation

$$-\Delta u+V(x)u=f(u) \ \ \textrm{in} \ \ \mathbb{R}^N \eqno{(P)}$$
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.

 
Next we study the same problem, but now considering $V$ being a non-periodic potential and the nonlinearity $f$ having asymptotically linear behavior at infinity. For the existence of a non-trivial solution, spectral theory is used and through the interactions of the translated solutions of the problem at infinity, the problem satisfies the geometry of the Linking Theorem with the Cerami condition.

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
Notícia cadastrada em: 20/06/2024 23:29
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