Um estudo sobre condições para existência e multiplicidade de soluções para problemas do tipo Ambrosetti-Prodi

• Main Author: Becker, Alex Jenaro
• Publication Date: 2015
• Format: Master thesis
• Language: por
• Source: Manancial - Repositório Digital da UFSM
• Download full: http://repositorio.ufsm.br/handle/1/17481
• topic: Problema do tipo Ambrosetti-Prodi; Métodos variacionais; Métodos topológicos; Estimativas a priori; Existência e multiplicidade de soluções; Varational methods; Topology methods; A priori bounds; Existence and multiplicity of solutions; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

The aim of this work is to establish conditions for the existence and multiplicity of solutions for Ambrosetti-Prodi problems type involving pLaplacian operator with subcritical growth related to the Sobolev critical exponent. In the development of this study, we were used the varational methods, such as, the Principle Varational Ekeland and the Mountain Pass Theorem, as well as topological methods, such as, the sub and supersolution method, a priori bounds and a generalization of theory of Leray-Schauder Topologic Degree. We determined parameters t����� < 0 < t+ t such that the proposed problem at has least two solutions for t t�����, at has least four solutions for t 2 [t�����; t+], at has least one solution for t t and no has solution for t > t .