Existência e multiplicidade de soluções de problemas elípticos com termo semilinear côncavo-convexo

• Autor(a) principal: Guimarães , Angelo
• Data de Publicação: 2017
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UFG
• dARK ID: ark:/38995/0013000008fxt
• Texto Completo: http://repositorio.bc.ufg.br/tede/handle/tede/6901
• topic: Problemas elipticos quasilineares; Termo semilinear concavoconvexo; Expoente crítico de Sobolev,; Mutiplicidade; Métodos variacionais; Quasilinear eliptic problems; Oncave-convex semilinear term; c; Sobolev critical expoent; Multiplicity; Variational methods; CIENCIAS EXATAS E DA TERRA::MATEMATICA

In 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.