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http://hdl.handle.net/10183/24519
Título | Soluções de equações p-sublineares envolvendo o operador p-Laplaciano via teoria de Morse |
Autor |
Stoffel, Augusto Ritter
|
Orientador |
Bonorino, Leonardo Prange
|
Data | 2010 |
Nível | Mestrado |
Instituição | Universidade Federal do Rio Grande do Sul. Instituto de Matemática. Programa de Pós-Graduação em Matemática. |
Assunto |
Equações diferenciais parciais
Teoria de Morse [en] Morse theory [en] Partial differential equations [en] p-Laplacian |
Resumo | Neste trabalho, estudamos a existˆencia e multiplicidade de solu¸c˜oes de certos problemas p-sublineares envolvendo o operador p-laplaciano usando teoria de Morse. |
Abstract | The purpose of this text is to provide a didactic exposition of the paper “Solutions of p-sublinear p-Laplacian equation via Morse theory” by Yuxia Guo and Jiaquan Liu [8]. This paper addresses the existence and multiplicity of solutions for the problem where is a smooth, bounded domain of RN, p is the p-Laplacian operator and f satisfies certain conditions, in particular f is p-sublinear at 0. Morse theory is used to infer the existence of critical points of a functional associated to this problem. In Chapter 2, we introduce the necessary Morse theoretic concepts, assuming basic knowledge of singular homology theory. In Chapter 3, we introduce basic properties of the p-Laplacian operator, assuming knowledge of Sobolev spaces, including imbedding and compactness results. Finally, in Chapter 4, we follow Guo and Liu’s paper itself. |
Tipo | Dissertação |
URI | http://hdl.handle.net/10183/24519 |
Arquivos | Descrição | Formato | |
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000747596.pdf (490.7Kb) | Texto completo | Adobe PDF | Visualizar/abrir |
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