Localization phenomena in a degenerate logistic equation
| dc.contributor.author | Arrieta Algarra, José María | |
| dc.contributor.author | Pardo San Gil, Rosa María | |
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.date.accessioned | 2023-06-19T14:56:22Z | |
| dc.date.available | 2023-06-19T14:56:22Z | |
| dc.date.issued | 2014 | |
| dc.description | Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems (2012) | |
| dc.description.abstract | We analyze the behavior of positive solutions of elliptic equations with a degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonlinearity cancels. This type of nonlinearity has applications in the nonlinear Schrodinger equation and the study of Bose–Einstein condensates. In this context, our analysis explains the fact that the ground state presents a strong localization in the spatial region in which the nonlinearity cancels. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Grupo de Investigación CADEDIF, Spain | |
| dc.description.sponsorship | Grupo 920894 BSCH-UCM | |
| dc.description.sponsorship | GR35/10-A | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/33235 | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.officialurl | http://ejde.math.txstate.edu/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/34875 | |
| dc.journal.title | Electronic Journal of Differential Equations, Conference 21 | |
| dc.language.iso | eng | |
| dc.page.final | 9 | |
| dc.page.initial | 1 | |
| dc.publisher | Department of Mathematics Texas State University | |
| dc.relation.projectID | MTM2009-07540 | |
| dc.relation.projectID | MTM2012-31298 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Localization phenomena in a degenerate logistic equation | |
| dc.type | journal article | |
| dc.volume.number | 21 | |
| dcterms.references | H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces SIAM Rev., 18, 620-709 (1976). J. M. Arrieta, R. Pardo and A. Rodríguez-Bernal. Asymptotic behavior of degenerate logistic equations. In Preparation. J.M. Arrieta, Domain Dependence of Elliptic Operators in Divergence Form, Resenhas IMEUSP, Vol. 3, No. 1, 107 - 123 (1997). I. Babushka and Viborny Continuous dependence of eigenvalues on the domains, Czechoslovak Math. J. 15 (1965), 169-178. R. Courant, D. Hilbert Method of Mathematical Physics, Vol. 1, Wiley- Interscience, New York, 1953 D. Daners, Dirichlet problems on varying domains, Journal of Differential Equations 188 (2003), no. 2, 591-624. J. M. Fraile, P. Koch Medina, J. López-Gómez, and S. Merino. Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equation. J. Differential Equations, 127(1):295–319, 1996. J. L. Gámez. Sub- and super-solutions in bifurcation problems. Nonlinear Anal., 28(4), 625–632, 1997. J. García-Melián, R. Gómez-Reñasco, J. López-Gómez, and J. C. Sabina de Lis. Pointwise growth and uniqueness of positive solutions for a class of sublinear elliptic problems where bifurcation from infinity occurs. Arch. Ration. Mech. Anal., 145(3):261–289, 1998. J. García-Melián, R. Letelier-Albornoz, and J. Sabina de Lis. Uniqueness and asymptotic behaviour for solutions of semilinear problems with boundary blow-up. Proc. Amer. Math. Soc., 129(12):3593–3602 (electronic), 2001. R. Gómez-Reñasco. The effect of varying coefficients in semilinear elliptic boundary value problems. From classical solutions to metasolutions, Ph D Dissertation, Universidad de La Laguna, Tenerife, March 1999. R. Gómez-Reñasco and J. López-Gómez, On the existence and numerical computation of classical and non-classical solutions for a family of elliptic boundary value problems Nonlinear Analysis: Theory, Methods & Applications, 48(4), 2002. A. Henrot, Extremum Problems for Eigenvalues of Elliptic Operators, Birkhäuser Verlag (2006) J. B. Keller. On solutions of ∆u = f(u). Comm. Pure Appl. Math., 10:503–510, 1957. J. López-Gómez and J. C. Sabina de Lis. First variations of principal eigenvalues with respect to the domain and point-wise growth of positive solutions for problems where bifurcation from infinity occurs. J. Differential Equations, 148(1):47–64, 1998. J. López-Gómez Metasolutions: Malthus versus Verhulst in population dynamics. A dream of Volterra, Stationary partial differential equations. Vol. II, Handb. Differ. Equ., 211–309, Elsevier/North-Holland, Amsterdam, (2005) Ouyang, Tiancheng, On the positive solutions of semilinear equations ∆u + λu − hup = 0 on the compact manifolds, Trans. Amer. Math. Soc., 331(2), 503–527, 1992 R. Osserman. On the inequality ∆u ≥ f(u). Pacific J. Math., 7:1641–1647, 1957. V. M. Pérez-García and R. Pardo. Localization phenomena in nonlinear Schrdinger equations with spatially inhomogeneous nonlinearities: theory and applications to Bose-Einstein condensates. Phys. D, 238(15):1352–1361, 2009. J. Smoller, Shock waves and reaction-diffusion equations. Grundlehren der Mathematischen Wissenschaften 258. Springer-Verlag, New York-Berlin, 1983 | |
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