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Applications of topological degree theory to generalized ODEs
(Universidade Federal de São Carlos, 2019-10-27)
In this work, we present original results concerning the theory of Generalized Ordinary Differential Equations (we write generalized ODEs for short) using tools from the Topological Degree theory. In particular, we proved ...
Ações de Z2k com o conjunto de pontos fixos conexo e a propriedade CP
(Universidade Federal de São Carlos, 2021-10-27)
It is well known that if $\phi:G \times M^m \rightarrow M^m$ is a smooth action of a compact Lie group on a closed smooth manifold, then its fixed point set $F_{\phi} = \bigcup\limits_{i=0}^{n}F^{i}$ is a disjoint union ...
Pseudo-parallel immersions of Lorentzian manifolds in pseudo-Riemannian space forms
(Universidade Federal de São Carlos, 2024-05-24)
In this Ph.D. thesis, we study pseudo-parallel submanifolds in pseudo-Riemannian space forms. We give a characterization of pseudo-parallel Lorentzian surfaces with non-flat normal bundle in pseudo-Riemannian space forms ...
Poliedros de Newton e invariantes de singularidades determinantais
(Universidade Federal de São Carlos, 2024-01-31)
In this work, we study invariants of determinantal singularities, by analysing the Newton polyhedra which arise from the entries of a given matrix. The main contribution of this work is providing sufficient conditions, ...
Equações elípticas com o Laplaciano fracionário e não linearidades indefinidas
(Universidade Federal de São Carlos, 2024-04-24)
In this work, we investigate the existence, non-existence and multiplicity of positive solutions of the problem below,
\begin{equation*}
\left\lbrace \begin{array}{rll}
(-\Delta)^s u -\lambda u & = f(x)g(u) ,& ...
Extensões H-cleft distinguidas por H-identidades polinomiais
(Universidade Federal de São Carlos, 2022-05-27)
Our main object of study is the well-known question asking whether the set of polynomials identities distinguishes PI-algebras up to isomorphism. Let k be an algebraically closed field of characteristic 0 and H a non-semisimple ...
Comportamento assintótico para equações de placa fracionárias
(Universidade Federal de São Carlos, 2024-07-16)
In this work, we consider two second-order fractional semilinear plate equations in time. In the first problem, we investigate an equation governed by a biharmonic operator, with clamped boundary conditions in a smooth ...
Lebesgue solvability of equations associated to elliptic and canceling linear differential operators with measure data
(Universidade Federal de São Carlos, 2024-04-10)
In this thesis, we present new results on the solvability of the equation A*(x,D) f = µ for f in L^p, with complex measure data µ, associated to an elliptic linear differential operator A(x,D) of order m with variable ...
Minimalidade de coincidências do tipo Borsuk-Ulam em superfícies utilizando tranças
(Universidade Federal de São Carlos, 2024-07-18)
Given topological spaces $M$ and $N$, with $M$ equipped with a free involution $\tau$, we define the set of Borsuk-Ulam coincidences as
$$
\operatorname{BUCoin}(f; \tau) = \{ \{ x, \tau(x) \} \ | \ f(x) = f(\tau(x)) ...
Sequência espectral persistente de Leray e propriedades de separação para variedades generalizadas
(Universidade Federal de São Carlos, 2024-08-22)
In this thesis we work on two different topics. On the one hand, we manage to construct a spectral sequence that calculates the persistent cohomology of a space from the persistent cohomology in each open and its interceptions ...