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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Teoria de bifurcação e aplicações / Bifurcation theory and applications

Rodriguez Villena, Diana Yovani [UNESP] 08 August 2017 (has links)
Submitted by DIANA YOVANI RODRÍGUEZ VILLENA null (dayaniss_23@hotmail.com) on 2017-10-09T19:16:47Z No. of bitstreams: 1 Dissertação Diana.pdf: 1051753 bytes, checksum: df5c2679c43a774ec3d6809c69271fd4 (MD5) / Approved for entry into archive by Monique Sasaki (sayumi_sasaki@hotmail.com) on 2017-10-09T19:43:34Z (GMT) No. of bitstreams: 1 rodriguezvillena_dy_me_sjrp.pdf: 1051753 bytes, checksum: df5c2679c43a774ec3d6809c69271fd4 (MD5) / Made available in DSpace on 2017-10-09T19:43:34Z (GMT). No. of bitstreams: 1 rodriguezvillena_dy_me_sjrp.pdf: 1051753 bytes, checksum: df5c2679c43a774ec3d6809c69271fd4 (MD5) Previous issue date: 2017-08-08 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho, estudamos a teoria de bifurcação e algumas das suas aplicações. Apresentamos alguns resultados básicos e definimos o conceito de ponto de bifurcação. Logo, estudamos a teoria do grau topológico. Em seguida, enunciamos dois teoremas importantes que são os teoremas de Krasnoselski e de Rabinowitz. Finalmente apresentamos um exemplo e duas aplicações do teorema de Rabinowitz nas quais os valores característicos com que lidamos são simples, no exemplo se consegue provar que a segunda alternativa do teorema ocorre, a primeira aplicação é um problema de autovalores não lineares de Sturm-Liouville para uma E.D.O de segunda ordem na qual se prova que a primeira alternativa do teorema de Rabinowitz é válida e a segunda aplicação é um problema de autovalores para uma equação diferencial parcial quase-linear a qual se prova que também ocorre a primeira alternativa do teorema. / In this work, we study bifurcation theory and its applications. We present some basic results and define the concept of bifurcation point. Then we study the theory of topological degree. Next we state two important theorems that are Krasnoselski's theorem and Rabinowitz's theorem. Finally we present an example and two applications of Rabinowitz theorem in which the characteristic values we deal with are simple, in an example we can prove that the second item of theorem occurs and the first application is a nonlinear Sturm-Liouville eigenvalue problem for a second order ordinary differential equation were we prove that the first alternative of Rabinowitz's theorem holds and the second application is an eigenvalue problem for a quasilinear elliptic partial differential equation where we prove that the first alternative of the theorem also holds.

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