Existence of positive solutions for a Semipositone fractional p-Laplacian problem
dc.contributor.advisor | Lopera Arias, Emer de Jesus | |
dc.contributor.author | López Morales, Camila | |
dc.date.accessioned | 2023-04-26T03:58:33Z | |
dc.date.available | 2023-04-26T03:58:33Z | |
dc.date.issued | 2023 | |
dc.description.abstract | In this thesis we will make a brief study of Fractional Sobolev spaces. We will give two equivalent de nitions of these spaces using interpolation spaces and the Fourier transform in the case p = 2. Finally, we prove the existence of at least one positive solution for the nonlocal semipositone problem. (Texto tomado de la fuente) | eng |
dc.description.abstract | En esta tesis haremos un breve estudio de los espacios Fraccionarios de Sobolev. Daremos dos de finiciones equivalentes de estos espacios usando espacios de interpolación y la transformada de Fourier en el caso p = 2. Finalmente, probaremos la existencia de al menos una solución positiva para el problema semipositón no local | spa |
dc.description.curriculararea | Matemáticas Y Estadística.Sede Manizales | spa |
dc.description.degreelevel | Maestría | spa |
dc.description.degreename | Magíster en Ciencias - Matemática Aplicada | spa |
dc.format.extent | 69 páginas | spa |
dc.format.mimetype | application/pdf | spa |
dc.identifier.instname | Universidad Nacional de Colombia | spa |
dc.identifier.reponame | Repositorio Institucional Universidad Nacional de Colombia | spa |
dc.identifier.repourl | https://repositorio.unal.edu.co/ | spa |
dc.identifier.uri | https://repositorio.unal.edu.co/handle/unal/83784 | |
dc.language.iso | eng | spa |
dc.publisher | Universidad Nacional de Colombia | spa |
dc.publisher.branch | Universidad Nacional de Colombia - Sede Manizales | spa |
dc.publisher.faculty | Facultad de Ciencias Exactas y Naturales | spa |
dc.publisher.place | Manizales, Colombia | spa |
dc.publisher.program | Manizales - Ciencias Exactas y Naturales - Maestría en Ciencias - Matemática Aplicada | spa |
dc.relation.references | Adams, Robert A.; Fournier, John J. F. Sobolev spaces. Second edition. Pure and Applied Mathematics (Amsterdam), 140. Elsevier/Academic Press, Am- sterdam, 2003. xiv+305 pp. ISBN: 0-12-044143-8 | spa |
dc.relation.references | Alves, Claudianor O.; de Holanda, Angelo R. F.; Santos, Jefferson A. Exis- tence of positive solutions for a class of semipositone quasilinear problems through Orlicz-Sobolev space. Proc. Amer. Math. Soc. 147 (2019), no. 1, 285–299 | spa |
dc.relation.references | Aronszajn, N. (1955). Boundary values of functions with finite Dirichlet integral. Techn. Report of Univ. of Kansas, 14, 77-94 | spa |
dc.relation.references | Badiale, Marino; Serra, Enrico. Semilinear elliptic equations for beginners. Existence results via the variational approach. Universitext. Springer, Lon- don, 2011. x+199 pp. ISBN: 978-0-85729-226-1 | spa |
dc.relation.references | Barb, Simona. Topics in geometric analysis with applications to partial dif- ferential equations. Thesis (Ph.D.)–University of Missouri - Columbia. Pro- Quest LLC, Ann Arbor, MI, 2009. 238 pp. ISBN: 978-1124-67385-1 | spa |
dc.relation.references | Biler, Piotr; Karch, Grzegorz; Woyczy ́nski, Wojbor A. Critical nonlinearity exponent and self-similar asymptotics for L ́evy conservation laws. Ann. Inst. H. Poincar ́e C Anal. Non Lin ́eaire 18 (2001), no. 5, 613–637 | spa |
dc.relation.references | Brezis, Haim. Functional analysis, Sobolev spaces and partial differential equations. Universitext. Springer, New York, 2011. xiv+599 pp. ISBN: 978- 0-387-70913-0 | spa |
dc.relation.references | Brown, K. J.; Shivaji, R. Simple proofs of some results in perturbed bi- furcation theory. Proc. Roy. Soc. Edinburgh Sect. A 93 (1982/83), no. 1-2, 71–82 | spa |
dc.relation.references | Caldwell, Scott; Castro, Alfonso; Shivaji, Ratnasingham; Unsurangsie, Sumalee. Positive solutions for classes of multiparameter elliptic semiposi- tone problems. Electron. J. Differential Equations 2007, No. 96, 10 pp | spa |
dc.relation.references | Castillo, Ren ́e Erl ́ın; Trousselot, Eduard. Reverse generalized H ̈older and Minkowski type inequalities and their applications. Bol. Mat. 17 (2010), no. 2, 137–142 | spa |
dc.relation.references | Castro, Alfonso; de Figueredo, Djairo G.; Lopera, Emer. Existence of pos- itive solutions for a semipositone p-Laplacian problem. Proc. Roy. Soc. Ed- inburgh Sect. A 146 (2016), no. 3, 475–482. | spa |
dc.relation.references | Dacorogna, Bernard. Introduction to the calculus of variations. Third edi- tion. Imperial College Press, London, 2015. x+311 pp. ISBN: 978-1-78326- 551-0 | spa |
dc.relation.references | Dhanya, R.; Tiwari, Sweta. A multiparameter fractional Laplace problem with semipositone nonlinearity. Commun. Pure Appl. Anal. 20 (2021), no. 12, 4043–4061 | spa |
dc.relation.references | Di Nezza, Eleonora; Palatucci, Giampiero; Valdinoci, Enrico. Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012), no. 5, 521–573 | spa |
dc.relation.references | Del Pezzo, Leandro M.; Quaas, Alexander. A Hopf’s lemma and a strong minimum principle for the fractional p-Laplacian. J. Differential Equations 263 (2017), no. 1, 765–778 | spa |
dc.relation.references | Demengel, Fran ̧coise; Demengel, Gilbert. Functional spaces for the theory of elliptic partial differential equations. Translated from the 2007 French original by Reinie Ern ́e. Universitext. Springer, London; EDP Sciences, Les Ulis, 2012. xviii+465 pp. ISBN: 978-1-4471-2806-9; 978-2-7598-0698-0 | spa |
dc.relation.references | Driver, B. K. (2003). Analysis tools with applications. Lecture notes | spa |
dc.relation.references | Duvaut, G.; Lions, J.-L. Inequalities in mechanics and physics. Trans- lated from the French by C. W. John. Grundlehren der Mathematischen Wissenschaften, 219. Springer-Verlag, Berlin-New York, 1976. xvi+397 pp. ISBN: 3-540-07327-2 | spa |
dc.relation.references | Edmunds, D. E.; Evans, W. D. Fractional Sobolev spaces and inequali- ties. Cambridge Tracts in Mathematics, 230. Cambridge University Press, Cambridge, 2023. ix+157 pp. ISBN: 978-1-009-25463-2 | spa |
dc.relation.references | Evans, Lawrence C. Partial differential equations. Second edition. Graduate Studies in Mathematics, 19. American Mathematical Society, Providence, RI, 2010. xxii+749 pp. ISBN: 978-0-8218-4974-3 | spa |
dc.relation.references | Fefferman, C.; de la Llave, R. Relativistic stability of matter. I. Rev. Mat. Iberoamericana 2 (1986), no. 1-2, 119–213 | spa |
dc.relation.references | Fiscella, Alessio; Servadei, Raffaella; Valdinoci, Enrico. Density properties for fractional Sobolev spaces. Ann. Acad. Sci. Fenn. Math. 40 (2015), no. 1, 235–253 | spa |
dc.relation.references | Gagliardo, Emilio. Propriet`a di alcune classi di funzioni in pi`u variabili. (Italian) Ricerche Mat. 7 (1958), 102–137 | spa |
dc.relation.references | Iannizzotto, Antonio; Mosconi, Sunra; Squassina, Marco. Global H ̈older regularity for the fractional p-Laplacian. Rev. Mat. Iberoam. 32 (2016), no. 4, 1353–1392 | spa |
dc.relation.references | Iannizzotto, Iannizzotto, Antonio; Mosconi, Sunra J. N.; Squassina, Marco. Fine boundary regularity for the degenerate fractional p-Laplacian. J. Funct. Anal. 279 (2020), no. 8, 108659, 54 pp | spa |
dc.relation.references | ones, Frank. Lebesgue integration on Euclidean space. Jones and Bartlett Publishers, Boston, MA, 1993. xvi+588 pp. ISBN: 0-86720-203-3 | spa |
dc.relation.references | Lunardi, Alessandra. Interpolation theory. Third edition [of MR2523200]. Appunti. Scuola Normale Superiore di Pisa (Nuova Serie) [Lecture Notes. Scuola Normale Superiore di Pisa (New Series)], 16. Edizioni della Normale, Pisa, 2018. xiv+199 pp. ISBN: 978-88-7642-639-1; 978-88-7642-638-4 | spa |
dc.relation.references | Mosconi, Sunra; Perera, Kanishka; Squassina, Marco; Yang, Yang. The Brezis-Nirenberg problem for the fractional p-Laplacian. Calc. Var. Partial Differential Equations 55 (2016), no. 4, Art. 105, 25 pp | spa |
dc.relation.references | Munkres, James R. Analysis on manifolds. Addison-Wesley Publishing Company, Advanced Book Program, Redwood City, CA, 1991. xiv+366 pp. ISBN: 0-201-51035-9 | spa |
dc.relation.references | Restrepo Montoya, D. E. (2018). On the fractional Laplacian and nonlocal operators. Escuela de Matem ́aticas | spa |
dc.relation.references | Rudin, Walter. Reelle und komplexe Analysis. (German) [[Real and com- plex analysis]] Translated from the third English (1987) edition by Uwe Krieg. R. Oldenbourg Verlag, Munich, 1999. xiv+499 pp. ISBN: 3-486-24789- 1 | spa |
dc.relation.references | Slobodeckij, L. N. (1958). Generalized Sobolev spaces and their applications to boundary value problems of partial differential equations, Leningrad. Gos. Ped. Inst. Ucep. Zap, 197, 54-112 | spa |
dc.relation.references | Tankov, P. (2003). Financial modelling with jump processes. Chapman and Hall/CRC | spa |
dc.rights.accessrights | info:eu-repo/semantics/openAccess | spa |
dc.rights.license | Reconocimiento 4.0 Internacional | spa |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | spa |
dc.subject.ddc | 510 - Matemáticas::515 - Análisis | spa |
dc.subject.proposal | Teorema de Paso de Montaña | spa |
dc.subject.proposal | Problema Semipositón | spa |
dc.subject.proposal | Soluciones positivas | spa |
dc.subject.proposal | p-Laplaciano fraccionario | spa |
dc.subject.proposal | Principios de comparación | spa |
dc.subject.proposal | Mountain pass theorem | eng |
dc.subject.proposal | Semipositone problem | eng |
dc.subject.proposal | Positive solutions | eng |
dc.subject.proposal | Fractional p-Laplacian | eng |
dc.subject.proposal | Comparison principles | eng |
dc.subject.unesco | Matemáticas | spa |
dc.subject.unesco | Mathematics | eng |
dc.subject.unesco | Matemáticas aplicadas | spa |
dc.subject.unesco | Teoremas matemáticos | spa |
dc.subject.unesco | Ecuaciones diferenciales no lineales | spa |
dc.title | Existence of positive solutions for a Semipositone fractional p-Laplacian problem | eng |
dc.title.translated | Existencia de soluciones positivas para un problema Semipositón con p-Laplaciano fraccionario | spa |
dc.type | Trabajo de grado - Maestría | spa |
dc.type.coar | http://purl.org/coar/resource_type/c_bdcc | spa |
dc.type.coarversion | http://purl.org/coar/version/c_ab4af688f83e57aa | spa |
dc.type.content | Text | spa |
dc.type.driver | info:eu-repo/semantics/masterThesis | spa |
dc.type.version | info:eu-repo/semantics/acceptedVersion | spa |
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