Banca de DEFESA: HUGO HENRYQUE COÊLHO E SILVA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
DISCENTE: HUGO HENRYQUE COÊLHO E SILVA
DATA : 12/02/2026
HORA: 14:00
LOCAL: Sala 209
TÍTULO:

On Nodal Solutions and Morse Index Estimates for Elliptic Systems

 

PALAVRAS-CHAVES:

Variational methods; Radial nodal solutions; FitzHugh-Nagumo system; Critical exponential growth.

 

PÁGINAS: 100
RESUMO:

In this thesis we study the existence, multiplicity, and qualitative structure of nodal solutions for several classes of semilinear elliptic systems, with particular emphasis on radial symmetry and prescribed nodal patterns. Our analysis is developed along three main directions. First, for FitzHugh-Nagumo type systems, a nonlocal  reformulation obtained by eliminating the second equation makes it possible to combine a radial domain decomposition with the Mountain Pass Theorem and a constrained Nehari manifold on annular subdomains. This yields, for every integer k, a radial solution whose first component exhibits exactly k nodal regions. The method applies both to subcritical Sobolev growth and to the critical exponential regime in the two-dimensional unit ball, where the Trudinger-Moser inequality plays a key role. In the second part, we consider a weakly coupled class of elliptic systems with powertype nonlinearities. Employing global deformation arguments on suitably chosen subsets of the Nehari manifold, we obtain existence and multiplicity of radial nodal solutions for which the number of sign changes of each component can be prescribed independently. Finally, for a broader class of gradient systems, we derive a lower bound for the Morse index of radial nodal solutions in terms of their nodal structure. The argument relies on a spectral decomposition of the associated linearized operators, linking the radial spectrum to the eigenvalues of the Laplace-Beltrami operator on the unit sphere.

 

 

MEMBROS DA BANCA:
Externo à Instituição - EUDES MENDES BARBOZA - UFRPE
Externa à Instituição - EVELINA SHAMAROVA - UFPB
Externo à Instituição - EVERALDO SOUTO DE MEDEIROS - UFPB
Externo à Instituição - JONISON LUCAS DOS SANTOS CARVALHO - UFS
Interno - 3089460 - JOSE CARLOS DE ALBUQUERQUE MELO JUNIOR