Problemas elípticos não lineares envolvendo equações do tipo Kirchhoff

• Ano de defesa: 2016
• Autor(a) principal: Guimarães, Mateus Balbino
• Orientador(a): Rodrigues, Rodrigo da Silva
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de São Carlos; Câmpus São Carlos
• Programa de Pós-Graduação: Programa de Pós-Graduação em Matemática - PPGM
• Palavras-chave em Português: Métodos variacionais; Expoentes críticos; Equações do tipo Kirchhoff; Equações elípticas não lineares
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: https://repositorio.ufscar.br/handle/20.500.14289/7755

In this work we study the existence of weak solutions for four nonlinear elliptic problems of Kirchhoff type. These problems have in common the presence of a function M : R+ [ f0g ! R+; known as Kirchhoff-type function. The first problem deals with a Kirchhoff type equation involving subcritical exponents while the second problem deals with the same equation but with a critical Caffarelli-Kohn-Nirenberg exponent. In the third problem, we study a system of Kirchhoff type equations involving critical Caffarelli-Kohn-Nirenberg exponents. The latter problem involves a Kirchhoff type operator and a nonlinear boundary condition. Due to the presence of the Kirchhoff type operator in the equations, these problems are called nonlocal problems. This phenomenon causes some mathematical difficulties, which makes the study of such a class of problem, particularly interesting. In our studies we used classical variational methods such as The Mountain Pass Theorem and the Krasnoseslkii genus theory.