2017-03-062017-03-01GUIMARÃES, Angelo. Existência e multiplicidade de soluções de problemas elípticos com termo semilinear côncavo-convexo. 2017. 67 f. Dissertação (Mestrado em Matemática) - Universidade Federal de Goiás, Goiânia, 2017.http://repositorio.bc.ufg.br/tede/handle/tede/6901In this work we study existence and multiplicity of weak solutions for the eliptic problem with semilinear concave convex term, in a limited domain of a N-dimensional euclidean space. If we take f=0 and σ=1 we have a problem homogeneous with critical Sobolev exponent in which we use the Mountain Pass Theorem to find existence of a solution when p<q<p* , and when 1<q<p we use the genus of Krasnoselskii finding infinitely many solutions. If f is not null and σ=0 we have a non homogeneous problem that we prove to have infinitely many solutions, using a method developed by P. Rabinowitz.application/pdfAcesso AbertoProblemas elipticos quasilinearesTermo semilinear concavoconvexoExpoente crítico de Sobolev,MutiplicidadeMétodos variacionaisQuasilinear eliptic problemsOncave-convex semilinear termcSobolev critical expoentMultiplicityVariational methodsCIENCIAS EXATAS E DA TERRA::MATEMATICADissertação