Banca de DEFESA: Leandro Oliveira Rezende

Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.
STUDENT : Leandro Oliveira Rezende
DATE: 15/12/2023
TIME: 08:00
LOCAL: PPGMAT
TITLE:

A study of solutions for an elliptic problem with critical growth in the gradient

KEY WORDS:

Elliptic equations, critical growth, indefinite problem, Mountain Pass Theorem, lower and
upper solutions

PAGES: 75
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:

In this work, we study the solutions for the problem
− ∆u = c(x)u + ⎸∇u⎹
2
+ f(x), u ∈ H
0
1
(Ω) ∩ L
∞
(Ω),

in which Ω is a bounded domain of R , and , for some . Firstly,

N N ≥ 3 c, f ∈ L
q
(Ω) q >
N
2
based on Jeanjean and Quoirin (2016), we suppose c is allowed to change sign, c , ,
+≢ 0 f ≩ 0
μ > 0 constant, and, using a lower semicontinuity argument together with the Mountain Pass
Theorem, we find two distinct solutions for our problem. Then, based on De Coster and Fernández
(2020), supposing c ≨ 0 and μ > 0 constant, we find a necessary and sufficient condition such
that our problem has a solution. Finally, using the lower and upper solutions method, we show the
existence of solutions is kept when μ ∈ L .

COMMITTEE MEMBERS:
Externo à Instituição - CLAUDINEY GOULART - UFJF
Presidente - 1858575 - MANUELA CAETANO MARTINS DE REZENDE
Interno - 2307366 - MARCELO FERNANDES FURTADO
Interno - 2570378 - RICARDO RUVIARO