Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-15T12:49:10Z No. of bitstreams: 1 arquivototal.pdf: 1323834 bytes, checksum: 530efbd6b56f11c5cc1b4369c8c44888 (MD5) / Made available in DSpace on 2017-08-15T12:49:10Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1323834 bytes, checksum: 530efbd6b56f11c5cc1b4369c8c44888 (MD5) Previous issue date: 2016-02-29 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / In this work we establish existence, multiplicity and concentration of positive solutions for the following class of problem 8<: 􀀀div􀀀 2 ( jruj)ru + V (x) (juj)u = f(u); in RN; u 2 W1; (RN); u > 0 in RN; where N 2, is a positive parameter, ; V; f are functions satisfying technical conditions that will be presented throughout the thesis and (t) = Rjtj 0 (s)sds. The main tools used are Variational methods, Lusternik-Schnirelman of category, Penalization methods and properties of Orlicz-Sobolev spaces. / Neste trabalho estabelecemos resultados de existência, multiplicidade e concentração de soluções positivas para a seguinte classe de problemas quasilineares 8<: 􀀀div􀀀 2 ( jruj)ru + V (x) (juj)u = f(u); em RN; u 2 W1; (RN); u > 0 em RN; onde N 2, é um parâmetro positivo, ; V; f são funções satisfazendo condições técnicas que serão apresentadas ao longo da tese e (t) = Rjtj 0 (s)sds. As principais ferramentas utilizadas são os Métodos Variacionais, Categoria de Lusternik-Schnirelman, Método de Penalização e propriedades dos espaços de Orlicz-Sobolev.

The theory of homogenization allows to find for a given system of partial differential equations governing a model with a very complicated internal struc- ture a system governing a model without this structure, whose solution is in a certain sense an approximation of the solution of the original problem. In this thesis, methods of the theory of homogenization are applied to three sys- tems of partial differential equations. The first one governs a flow of a class of non-Newtonian fluid through a porous medium. The second system is utilized for modeling of a flow of a fluid through an electric field wherein the viscosity depends significantly on the intensity of the electric field. For the third system is considered an elliptic operator having growth and coercivity indicated by a general anisotropic inhomogeneous N-function. 1