Return to search

Problemas de auto- valor não- lineares: métodos topológicos, variacionais e um teorema geral de sub e super soluções / Nonlinear eigenvalue problems: variational, topological methods and a general theorem of the sub and supersolutions

Submitted 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) / Made 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: 2014-03-28 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In 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. / Neste 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.

Identiferoai:union.ndltd.org:IBICT/oai:repositorio.bc.ufg.br:tde/2977
Date28 March 2014
CreatorsSantos, Dassael Fabrício dos Reis
ContributorsGonçalves, José Valdo Abreu, Gonçalves, José Valdo Abreu, Santos, Carlos Alberto Pereira dos, Carvalho, Marcos Leandro Mendes
PublisherUniversidade Federal de Goiás, Programa de Pós-graduação em Matemática (IME), UFG, Brasil, Instituto de Matemática e Estatística - IME (RG)
Source SetsIBICT Brazilian ETDs
LanguagePortuguese
Detected LanguagePortuguese
Typeinfo:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/masterThesis
Formatapplication/pdf
Sourcereponame:Biblioteca Digital de Teses e Dissertações da UFG, instname:Universidade Federal de Goiás, instacron:UFG
Rightshttp://creativecommons.org/licenses/by-nc-nd/4.0/, info:eu-repo/semantics/openAccess
Relation6600717948137941247, 600, 600, 600, 600, -4268777512335152015, 8398970785179857790, -2555911436985713659, [1] ADAMS, R. A. SobolevSpaces. AcademicPress,NewYork, 1975. [2] AMBROSETTI, A.; ARCOYA, D. AnIntroductiontoNonlinearFunctionalAnalysis andEllipticProblems. Birkhauser, Berlin, 2012. [3] AMBROSETTI, A.; MALCHIODI, A. Nonlinear Analysis and Semilinear Elliptic Problems. CambridgeUniversityPress,NewYork, 2007. [4] BREZIS, H. FunctionalAnalysis,SobolevSpacesandPartialDifferentialEquations. Springer, NewYork, 2011. [5] BROWN, K. J.; BUDIN, V. H. Multiple positive solutions for a class of nonlinear boundaryvalueproblems. J. MathAnal.andApplications, 60:329–338, 1977. [6] BROWN, K. J.; BUDIN, V. H. On the existence of positive solutions for a class of semilinearellipticboundaryvalueproblems. J. MathAnal., 5:875–883,1979. [7] CARL, S.; LE, V. K.; MOTREANU, D. Nonsmoth Variational Problems and Their Inequalities: Comparison Principles and Applications. Springer, New York, 2005. [8] CUESTA, M. Existence results for quasilinear problems via ordered sub and supersolutions. Annales de la Faculté des Sciences de Toulouse, 6o Série no 4, 6:591–608,1997. [9] DANCER, E.; SCHMITT, K. Onpositivesolutionsofsemilinearellipticequations. Proceedings ofthe American Mathematical Society, 101:445–452,1987. [10] DEIMLING, K. NonlinearFunctionalAnalysis. Springer-Verlag, Berlim,1985. [11] DUNFORD, N.; SCHWARTZ, J. T. Linear Operators Part I: General Theory. Interscience Publishers,Inc, NewYork, 1957. [12] FIGUEIREDO, D. G. Equações Elípticas Não-Lineares. Instituto de Matemática Pura eAplicada, Rio de Janeiro, 1977. [13] FOLLAND, G. B. Introduction to Partial Differential Equations. Princeton UniversityPress,NewJersey, 1995. [14] GHERGU, M.; RADULESCU, V. Sublinear singular elliptic problems with two parameters. J. DifferentialEquation, 195:520–536,2003. [15] GILBARG,D.;TRUDINGER,N.S. EllipticPartialDifferentialEquationsofSecond Order. Springer, NewYork, 1983. [16] HAN, Q.; LIN, F. Elliptic Partial Differential Equations. Courant Institute of Mathematical Sciences, NewYork, 2000. [17] HESS, P. On multiple positive solutions of nonlinear elliptic eigenvalue problems. Commun.Partial DifferentialEquations, 6:951–961,1981. [18] KINDERLEHRER, D.; STAMPACCHIA, G. An Introduction to Variational InequalitiesandTheirApplications. AcademicPress,NewYork, 1980. [19] KURA, T. Theweaksupersolution-subsolutionmethodforsecondorderquasilinearallipticequations. HiroshimaMath.J., 19:1–36, 1989. [20] LE, V. K. On some equivalent properties of sub- and supersolutions in second orderquasilinearellipticequations. HiroshimaMath.J., 28:373–380, 1998. [21] LE, V. K. Subsolution-supersolutionsandtheexistenceofextremalsolutionsin noncoercivevariationalinequalities. JIPAM, 2:1–16,2001. [22] LE, V. K.; SCHMITT, K. Onboundaryvalueproblemsfordegeneratequasilinear ellipticequationsandinequalities. J. DifferentialEquations, 144:170–218,1998. [23] LE, V. K.; SCHMITT, K. 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.

Page generated in 0.0023 seconds