Problemas de auto- valor não- lineares: métodos topológicos, variacionais e um teorema geral de sub e super soluções

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dc.contributor.advisor1Gonçalves, José Valdo Abreu
dc.contributor.advisor1Latteshttp://lattes.cnpq.br/5148611284176776por
dc.contributor.referee1Gonçalves, José Valdo Abreu
dc.contributor.referee2Santos, Carlos Alberto Pereira dos
dc.contributor.referee3Carvalho, Marcos Leandro Mendes
dc.creatorSantos, Dassael Fabrício dos Reis
dc.creator.Latteshttp://lattes.cnpq.br/5585978357624914por
dc.date.accessioned2014-09-01T19:21:42Z
dc.date.available2014-09-01
dc.date.issued2014-03-28
dc.description.abstractIn this work we study existence and multiplicity of non-negative solutions of the nonlinear elliptic problem −div(A(x,∇u)) = λf(x,u) in Ω, u = 0 in ∂Ω where Ω⊂IRN is a bounded domain with smooth boundary∂Ω,λ≥ 0 is a parameter, f :Ω×[0,∞)−→ IR and A :Ω×IRN−→ IRN satisfy the Carathéodory conditions, A is monotone and f satisfies a growth condition. To this end we use the method of Sub and Supersolutions, Topological Degree Theory, simmetry arguments and variational methods.eng
dc.description.provenanceSubmitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2014-09-01T19:21:42Z No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dassael Fabricio dos Reis Santos - Dissertação de Mestrado.pdf: 2389476 bytes, checksum: 8ca3d9cabd2862c5e82bc4db0cec4071 (MD5)eng
dc.description.provenanceMade available in DSpace on 2014-09-01T19:21:42Z (GMT). No. of bitstreams: 2 license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Dassael Fabricio dos Reis Santos - Dissertação de Mestrado.pdf: 2389476 bytes, checksum: 8ca3d9cabd2862c5e82bc4db0cec4071 (MD5) Previous issue date: 2014-03-28eng
dc.description.resumoNeste trabalho estudaremos existência e multiplicidade de soluções não-negativas do problema elíptico não-linear −div(A(x,∇u)) = λf(x,u) em Ω, u = 0 em ∂Ω, Onde Ω ⊂ IRN é um domínio limitado com fronteira∂Ω suave,λ≥ 0 é um parâmetro, f :Ω×[0,∞)−→ IR e A :Ω×IRN−→ IRN satisfazem as condições de Carathéodory, A é monotônico e f satisfaz uma condição de crescimento. Para este fim utilizaremos o método de Sub e Super Soluções, Teoria do Grau Topológico, argumentos de simetria e métodos variacionais.por
dc.description.sponsorshipConselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPqpor
dc.formatapplication/pdf*
dc.identifier.citationSantos, Dassael Fabrício dos Reis - Problemas de auto- valor não- lineares: métodos topológicos, variacionais e um teorema geral de sub e super soluções - 2014 - 146 f.- Dissertação - Programa de Pós-graduação em Matemática (IME) - Universidade Federal de Goiás - Goiânia - Goiás - Brasil.por
dc.identifier.urihttp://repositorio.bc.ufg.br/tede/handle/tde/2977
dc.languageporpor
dc.publisherUniversidade Federal de Goiáspor
dc.publisher.countryBrasilpor
dc.publisher.departmentInstituto de Matemática e Estatística - IME (RG)por
dc.publisher.initialsUFGpor
dc.publisher.programPrograma de Pós-graduação em Matemática (IME)por
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Sub-supersolution theorems for quasilinear elliptic problems: A variational approach. Electron J. Differential Equations, 118:1–7, 2004. [24] LE, V. K.; SCHMITT, K. Some general concepts of sub-supersolutions for nonlinear elliptic problems. Topological Methods in Nonlinear Analysis, 28:87–103, 2006. [25] LIEBERMAN, G. M. The natural generalization of the natural conditions os ladyzhenskaya and ural’tseva for elliptic equations. Comm. Partial Differential Equations, 16:311–361, 1991. [26] LOC, N. H.; SCHMITT, K. Onpositivesolutionsofquasilinearellipticequations. DifferentialIntegralEquations, 22:829–842, 2009. [27] MEDEIROS, L. A.; MIRANDA, M. M. EspaçosdeSobolev(IniciaçãoaosProblemas Elípticos Não-Homogêneos). Instituto de Matemática - UFRJ, Rio de Janeiro, 2000. [28] O’REGAN, D.; CHO, Y. J.; CHEN, Y.-Q. TopologicalDegreeTheoryandApplications. Chapman and Hall/CRC, New York, 2006. [29] PERAL, I. Multiplicity of Solutions for the p-Laplacian. Second School of Nonlinear Functional Analysis and Applications to Differential Equations, Trieste, 1997. [30] RABINOWITZ, P. A note on topological degree for potential operators. J. Math. Anal.Appl., 51:483–492, 1975. [31] RUDIN, W. RealandComplexAnalysis. McGrawHillSeriesinHigherMathematics, New York, 2000. [32] SAKAGUCHI, S. Concavity properties of solutions to some degenerate quasilinear elliptic dirichlet roblems. Annali de la Scuola Normale Superiori di Pisa Classe diScienze4e Série, no 3, 14:403–421, 1987. [33] SCHMITT, K.; THOMPSON, R. C. NonlinearAnalysisandDifferentialEquations: AnIntroduction. http://www.math.utah.edu/ schmitt/ode1.pdf, 2004. [34] SCHWARTZ, J. T. Nonlinear Functional Analysis. Gordon and Breach Science Publishers, New York-London-Paris, 1969. [35] STAMPACCHIA, G. EquationsElliptiquesduSecondOrdreaCoefficientsDiscontinus. Les Presses de L’Universite de Montreal, Montreal, 1966. [36] TREVES, F. Basic Linear Partial Differential Equations. Pure and Applied MathematicsVol62. Academic Press, New York-London, 1975. [37] VÁZQUEZ, J. L. A strong maximum principle for some quasilinear elliptic equations. Appl.Math.Optim., 12:191–202, 1984.por
dc.rightsAcesso abertopor
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectProblemas Não-Linearespor
dc.subjectSub e Super Soluçõespor
dc.subjectGrauTopológicopor
dc.subjectMinimização,por
dc.subjectPrincípios de Máximopor
dc.subjectNonlinear Problemseng
dc.subjectSub and Supersolutionseng
dc.subjectTopological Degreeeng
dc.subjectMinimizationeng
dc.subject.cnpqMATEMATICA::MATEMATICA APLICADApor
dc.thumbnail.urlhttp://repositorio.bc.ufg.br/tede/retrieve/6947/Dassael%20Fabricio%20dos%20Reis%20Santos%20-%20Disserta%c3%a7%c3%a3o%20de%20Mestrado.pdf.jpg*
dc.titleProblemas de auto- valor não- lineares: métodos topológicos, variacionais e um teorema geral de sub e super soluçõespor
dc.title.alternativeNonlinear eigenvalue problems: variational, topological methods and a general theorem of the sub and supersolutionseng
dc.typeDissertaçãopor

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Mestrado Profissional em Matemática em Rede Nacional (IME)