Autor(es): Enguiça, Ricardo Mariano Roque Capela, 1978-
Data: 2010
Identificador Persistente: http://hdl.handle.net/10451/1953
Origem: Repositório da Universidade de Lisboa
Assunto(s): Problemas de valores na fronteira; Singularidades (Matemática); Métodos variacionais; Análise matemática; Teses de doutoramento - 2010
Tese de doutoramento, Matemática (Análise Matemática), Universidade de Lisboa, Faculdade de Ciências, 2010
We study the existence of solutions for a nonlocal singular second order ordinary differential equation. We obtain results through Krasnoselskii’s fixed point Theorem and using some properties of the eigenvalues of the underlying singular linear problem and, on a different approach, through the monotone method associated with well-ordered lower and upper solutions. We deal with second and fourth order problems in infinite intervals, where we prove the existence of an homoclinic or an heteroclinic solution. For the second order we consider both superlinear and bounded nonlinearities, and prove existence results through variational methods. A non-variational approach was made for a second order problem with a dissipative term and a p-laplacian problem was also adressed. Simpler fourth order bvp’s were also tackled from a variational point of view. We also analyse fourth order boundary value problems related to beam deflection theory, generalizing some well known results for the second order. We analysed two types of problems: the case where the correspondent fourth order operator can be decomposed in two positive second order operators and the case where that cannot be done. The results are obtained through topological arguments in association with lower and upper solutions.
Centro de Matemática e Aplicações Fundamentais (CMAF); PhD fellowship by Fundação para a Ciência e a Tecnologia (FCT)- ; FCT project POCI/MAT/57258/2004; ISEL
