Semilinear elliptic partial differential equations with the critical Sobolev exponent

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dc.contributor.advisorEbobisse Bille, Francoisen_ZA
dc.contributor.authorMavuso, Melusi Manqobaen_ZA
dc.date.accessioned2017-09-28T05:26:30Z
dc.date.available2017-09-28T05:26:30Z
dc.date.issued2017en_ZA
dc.description.abstractWe present how variational methods and results from linear and non-linear functional analysis are applied to solving certain types of semilinear elliptic partial differential equations (PDEs). The ultimate goal is to prove results on the existence and non-existence of solutions to the Semilinear Elliptic PDEs with the Critical Sobolev Exponent. To this end, we first recall some useful results from functional analysis, including the Sobolev spaces, which provide a natural setting for the idea of weak or generalised solutions. We then present linear PDE theory, including eigenvalues of the Dirichlet Laplacian operator. We discuss the Direct Methods of Calculus of Variations and Critical Point Theory, together with examples of how these techniques are applied to solving PDEs. We show how the existence of solutions to semilinear elliptic equations depends on the exponent of the growth of the non-linear term. This then naturally leads to the discussion of the critical Sobolev exponent, where we present both positive and negative results.en_ZA
dc.identifier.apacitationMavuso, M. M. (2017). <i>Semilinear elliptic partial differential equations with the critical Sobolev exponent</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics. Retrieved from http://hdl.handle.net/11427/25441en_ZA
dc.identifier.chicagocitationMavuso, Melusi Manqoba. <i>"Semilinear elliptic partial differential equations with the critical Sobolev exponent."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017. http://hdl.handle.net/11427/25441en_ZA
dc.identifier.citationMavuso, M. 2017. Semilinear elliptic partial differential equations with the critical Sobolev exponent. University of Cape Town.en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Mavuso, Melusi Manqoba AB - We present how variational methods and results from linear and non-linear functional analysis are applied to solving certain types of semilinear elliptic partial differential equations (PDEs). The ultimate goal is to prove results on the existence and non-existence of solutions to the Semilinear Elliptic PDEs with the Critical Sobolev Exponent. To this end, we first recall some useful results from functional analysis, including the Sobolev spaces, which provide a natural setting for the idea of weak or generalised solutions. We then present linear PDE theory, including eigenvalues of the Dirichlet Laplacian operator. We discuss the Direct Methods of Calculus of Variations and Critical Point Theory, together with examples of how these techniques are applied to solving PDEs. We show how the existence of solutions to semilinear elliptic equations depends on the exponent of the growth of the non-linear term. This then naturally leads to the discussion of the critical Sobolev exponent, where we present both positive and negative results. DA - 2017 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 2017 T1 - Semilinear elliptic partial differential equations with the critical Sobolev exponent TI - Semilinear elliptic partial differential equations with the critical Sobolev exponent UR - http://hdl.handle.net/11427/25441 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/25441
dc.identifier.vancouvercitationMavuso MM. Semilinear elliptic partial differential equations with the critical Sobolev exponent. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Mathematics and Applied Mathematics, 2017 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/25441en_ZA
dc.language.isoengen_ZA
dc.publisher.departmentDepartment of Mathematics and Applied Mathematicsen_ZA
dc.publisher.facultyFaculty of Scienceen_ZA
dc.publisher.institutionUniversity of Cape Town
dc.subject.otherMathematicsen_ZA
dc.titleSemilinear elliptic partial differential equations with the critical Sobolev exponenten_ZA
dc.typeMaster Thesis
dc.type.qualificationlevelMasters
dc.type.qualificationnameMScen_ZA
uct.type.filetypeText
uct.type.filetypeImage
uct.type.publicationResearchen_ZA
uct.type.resourceThesisen_ZA
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