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Métodos variacionais aplicados à problemas singulares em equações elípticas não lineares / Variational methods applied to singular problems in elliptic nonlinear equationsBrito, Lucas Menezes de 10 August 2018 (has links)
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Previous issue date: 2018-08-10 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we study a singular partial differential problem in a bounded domain
with smoth boundary. We have two main cases, one superlinear with weak
singularity, and the other one sublinear with strong songularity. We use
Variational Methods, such as the Ekeland Variational Principle and the Nehari
Manifolds, to solve this problem, finding weak solutions and proving the
multiplicity of solutions in one of the cases. / Neste trabalho estudaremos um problema diferencial parcial singular em um
domínio limitado com bordo suave. Temos dois casos principais, um superlinear
com singularidade fraca e um sublinear com singularidade forte. Usaremos
Métodos Variacionais, como o Princípio Variacional de Ekeland e as Variedades
de Nehari, para resolver este problema, encontrando soluções fracas e
provando a multiplicidade das mesmas em um dos casos.
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