2015-01-162014-06-23MARCIAL, Marcos Roberto. Estrutura topológica do conjunto de soluções de perturbações não lineares do p-laplaciano. 2014. 126 f. Tese (Doutorado em Matemática) - Universidade Federal de Goiás, Goiânia, 2014.http://repositorio.bc.ufg.br/tede/handle/tede/3901In this work, we study the topological structure of the solution set for a class of problems −Δpu = λ f (u)+μg(u)|∇u|p+Ψ(x) in Ω, u > 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ IRN is a bounded domain with ∂Ω smooth, p, λ, μ are constants with p > 1, λ ≥ 0, μ ∈ IR and f ,g : (0,∞)→IR Ψ : Ω→IR are continuous functions. We will use Variational and Topological Methods, which includes minimization of energy functional and building connected components of solutions in a sense that we will define. Also we will employ arguments about the theory of regularity for p-Laplacian operator, approach arguments , maximum principles, results about sub and supersolutions and also arguments including monotonic type operators.application/pdfAcesso AbertoSingularidadesOperador p-laplacianoSub e supersoluçõesGrau topológicoComponentes conexasPrincípios de máximoPontos fixosSingularitiesP-Laplacian operatorSub and supersolutionsTopological degreeConnected componentsPrinciples maximumFixed pointsCIENCIAS EXATAS E DA TERRA::MATEMATICATese