2024-10-022024-10-022024-06-20MARINHO, A. J. Cohomology and partial differential equations. 2024. 141 f. Dissertação (Mestrado em Matemática) - Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, 2024.http://repositorio.bc.ufg.br/tede/handle/tede/13453This text deals with elliptic partial differential equation problems by the Morse theoric point of view. Since Morse theory has a connection with some concepts from algebraic topology, cohomology theory is employed to show existence result for a class of equations. The concept of cohomological index will be useful to show multiple solution results for the Brezis-Nirenberg problem for the p-Laplacian.Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Morse theoryCohomological indexP-LaplacianBrezis-Niremberg problemElliptic partial differential equationsLinkingCritical pointsVariational methodsTeoria de MorseÍndice cohomológicoP-LaplacianoEquações diferenciais parciais elípticasEnlacePontos críticosMétodos variacionaisCIENCIAS EXATAS E DA TERRA::MATEMATICADissertação