ABP estimates and Ambrosetti-Prodi type problems for nonlinear differential operators / Estimativas ABP e problemas do tipo Ambrosetti-Prodi para operadores diferenciais não lineares

AUTOR(ES)

Taisa Junges Miotto

DATA DE PUBLICAÇÃO

2009

RESUMO

The aim of this work is to obtain ABP estimates for fully nonlinear operators and to study problems of the Ambrosetti-Prodi type for the p-Laplacian operator in two cases: superlinear case for the equation and the sublinear case for the system. For this, we use the sub and supersolution method and the Leray Schauder degree theory, to obtain in the two cases, multiplicity of solutions. To apply the degree theory, we need a priori estimates of the possible solutions, obtained applying di_erent techniques in each problem. In Chapter 1 we will cite some auxiliary results, which will use during this work. In Chapter 2 we will obtain ABP estimates for viscosity solutions to a class of fully nonlinear operators, whose example is the p_Laplacian operator. In Chapter 3 we will study the Ambrosetti-Prodi type problems for the superlinear case, using the blow up technique and Liouville theorems type. In Chapter 4 we will study the Ambrosetti-Prodi type problem for system in the sublinear case, using for this viscosity solutions and the variational characterization of the principal eigenvalue

ASSUNTO(S)

estimativas a-priori a priori estimates partial differential equations nonlinear differential equations equações diferenciais não-lineares equações diferenciais parciais

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