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Sobre Noções Restritivas de Lineabilidade

2026-06-02T13:04:15Z

Título: Sobre Noções Restritivas de Lineabilidade Autor: LUSTOSA, Ítalo Bruno Leandro Primeiro orientador: RAPOSO JÚNIOR, Anselmo Baganha Abstract: In this work, we gather and contextualize recent results on algebraic structures in nonlinear subsets of topological vector spaces, with emphasis on the notions of lineability, spaceability, and their stronger versions, such as (α, β)-lineability, (α, β)-spaceability, and the associated pointwise notions. Initially, we discuss general criteria for the strong notions of lineability and spaceability, establishing abstract conditions that explain the systematic failure of positive results when more restrictive requirements on dimension and closedness are imposed. We then present results on the set of continuous, integrable, and unbounded functions on [0,∞), showing that this set admits large-dimensional linear structures, including pointwise spaceability results, while also highlighting relevant limitations regarding (ℵ0,c)-spaceability. As applications, classical results in function and sequence spaces are recovered and generalized, revealing the delicate interplay between algebraic and topological properties in these contexts. Instituição: Universidade Federal do Maranhão Tipo do documento: Dissertação

Método de Nehari e aplicações

2026-05-29T13:37:48Z

Título: Método de Nehari e aplicações Autor: DIMARANES, Gleidson Filadelfo Primeiro orientador: MOREIRA NETO, Sandra Imaculada Abstract: In this work, we use the Nehari Method to show the existence of a Ground State solution for the following boundary value problem based in [9]...where Ω ⊂ R N denotes a bounded domain, ∆ is the Laplacian operator, and the nonlinearity f ∈ C1(R, R) satisfies suitable regularity and growth hypotheses, such as...for constants C > 0 and 2 < r < 2∗, where 2 ∗represents the critical Hardy-Sobolev exponent with value...We also apply Nehari’s Method to prove the existence of a nodal solution with minimum energy for the Kirchhoff-type problem proposed in [10] and described by where Ω ⊂ R3 is a smooth and bounded domain, and it is assumed that the nonlinearity f, as well as the nonlocal term M, satisfy adequate regularity and growth hypotheses. Instituição: Universidade Federal do Maranhão Tipo do documento: Dissertação

Rigidez de esferas mínimas com área 4π

2025-11-21T12:30:05Z

Título: Rigidez de esferas mínimas com área 4π Autor: CHAGAS, Larissa Santos Primeiro orientador: NUNES, Ivaldo Paz Abstract: In this work, we will prove two theorems due to Mazet and Rosenberg in (Mazet; Rosenberg, 2014). These results characterize a complete Riemannian 3-manifold M under certain conditions. The first theorem requires that a sectional curvature of M satisfies 0 ≤ K ≤ 1, and states that if a minimal embedded 2-sphere Σ in M has area |Σ| equal to 4π, then M is isometric to a canonical sphere (S 3 , gcan) with sectional curvature equal to 1 or a quotient of the product S 2 × R. The second theorem is a rigidity theorem for hyperbolic cusps in which M has sectional curvature K ≤ −1, and states that if T is a torus of constant mean curvature equal to 1 embedded in M then the convex side of T in M is isometric to T 2 × R+(hyperbolic cusp). Instituição: Universidade Federal do Maranhão Tipo do documento: Dissertação

Classes homoclínicas e medidas de máxima entropia

2025-11-13T12:07:38Z

Título: Classes homoclínicas e medidas de máxima entropia Autor: VALE, Maria Carla Bulhão de Queirós Andrade Primeiro orientador: COSTA, José Santana Campos Abstract: This research studies homoclinic classes and maximizing entropy measures, with the objective of presenting the proof of the main theorems and corollaries studied in the Article Shub’s example revisited [30]. The uniqueness of the maximum entropy measure for a class of perturbations of the original system was analyzed. The specific objectives are: to expose initial concepts and results relevant to the understanding of the main theorems, to present the main theorems and to explain the contributions of the work to the academic community. This is a bibliographic research. Instituição: Universidade Federal do Maranhão Tipo do documento: Dissertação