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Artículo
Semilinear problems with right-hand sides singular at u = 0 which change sign
dc.creator | Casado Díaz, Juan | es |
dc.creator | Murat, François | es |
dc.date.accessioned | 2022-11-11T08:25:30Z | |
dc.date.available | 2022-11-11T08:25:30Z | |
dc.date.issued | 2021-06-01 | |
dc.identifier.citation | Casado Díaz, J. y Murat, F. (2021). Semilinear problems with right-hand sides singular at u = 0 which change sign. Annales de l'Institut Henri Poincaré. Analyse non linéaire, 38 (3), 877-909. https://doi.org/10.1016/J.ANIHPC.2020.09.001. | |
dc.identifier.issn | 0294-1449 | es |
dc.identifier.issn | 1873-1430 | es |
dc.identifier.uri | https://hdl.handle.net/11441/139289 | |
dc.description.abstract | The present paper is devoted to the study of the existence of a solution u for a quasilinear second order differential equation with homogeneous Dirichlet conditions, where the right-hand side tends to infinity at u = 0u=0. The problem has been considered by several authors since the 70's. Mainly, nonnegative right-hand sides were considered and thus only nonnegative solutions were possible. Here we consider the case where the right-hand side can change sign but is non negative (finite or infinite) at u = 0u=0, while no restriction on its growth at u = 0u=0 is assumed on its positive part. We show that there exists a nonnegative solution in a sense introduced in the paper; moreover, this solution is stable with respect to the right-hand side and is unique if the right-hand side is nonincreasing in u. We also show that if the right-hand side goes to infinity at zero faster than 1/ |u|1/∣u∣, then only nonnegative solutions are possible. We finally prove by means of the study of a one-dimensional example that nonnegative solutions and even many solutions which change sign can exist if the growth of the right-hand side is 1/ |u|\right.^{\gamma }\right. with 0 < \gamma < 10<γ<1. | es |
dc.format | application/pdf | es |
dc.format.extent | 32 p. | es |
dc.language.iso | eng | es |
dc.publisher | Elsevier | es |
dc.relation.ispartof | Annales de l'Institut Henri Poincaré. Analyse non linéaire, 38 (3), 877-909. | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 Internacional | * |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | * |
dc.subject | Monotone operators | es |
dc.subject | Existence | es |
dc.subject | Singular equations | es |
dc.subject | Uniqueness | es |
dc.subject | Positive and nonpositive solutions | es |
dc.title | Semilinear problems with right-hand sides singular at u = 0 which change sign | es |
dc.type | info:eu-repo/semantics/article | es |
dcterms.identifier | https://ror.org/03yxnpp24 | |
dc.type.version | info:eu-repo/semantics/publishedVersion | es |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | es |
dc.contributor.affiliation | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico | es |
dc.relation.publisherversion | 10.1016/J.ANIHPC.2020.09.001 | es |
dc.identifier.doi | 10.1016/J.ANIHPC.2020.09.001 | es |
dc.contributor.group | Universidad de Sevilla. FQM309: Control y Homogeneización de Ecuaciones en Derivadas Parciales | es |
dc.journaltitle | Annales de l'Institut Henri Poincaré. Analyse non linéaire | es |
dc.publication.volumen | 38 | es |
dc.publication.issue | 3 | es |
dc.publication.initialPage | 877 | es |
dc.publication.endPage | 909 | es |
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