Stationary Sign Changing Solutions for an Inhomogeneous Nonlocal Problem

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dc.contributor.authorCortazar, Carmen
dc.contributor.authorElgueta, Manuel
dc.contributor.authorGarcia Melian, Jorge
dc.contributor.authorMartinez, Salome
dc.date.accessioned2024-01-10T12:08:47Z
dc.date.available2024-01-10T12:08:47Z
dc.date.issued2011
dc.description.abstractWe consider the following nonlocal equation:
dc.description.abstractintegral(R)J (x - y/g(y)) u(y)/g(y) dy - u(x) = 0 x epsilon R,
dc.description.abstractwhere J is an even, compactly supported, Holder continuous probability kernel, g is a continuous function, bounded and bounded away from zero in R. We prove the existence of a sign changing solution q(x) which is strictly positive when x > K and strictly negative for x < -K, provided that K is chosen large enough. The solution q(x) so constructed verifies a(1) <= q(x)/x <= a(2) for positive constants a(1), a(2) and large vertical bar x vertical bar. In addition, we show that all solutions with polynomial growth are of the form Aq(x) + Bp (x), where p is the unique normalized positive (bounded) solution of the equation. In the particular case where g = 1 we also construct solutions with exponential growth.
dc.description.funderMinisterio de Ciencia e Innovacion
dc.description.funderFEDER (Spain)
dc.description.funderFONDECYT
dc.description.funderBasal project CMM U. de Chile
dc.description.funderCAPDE Anillo (Chile)
dc.format.extent24 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1512/iumj.2011.60.4385
dc.identifier.eissn1943-5258
dc.identifier.issn0022-2518
dc.identifier.urihttps://doi.org/10.1512/iumj.2011.60.4385
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/76427
dc.identifier.wosidWOS:000303134000010
dc.information.autorucMatemática;Cortazar C;S/I;99550
dc.information.autorucMatemática;Elgueta M;S/I;99097
dc.issue.numero1
dc.language.isoen
dc.nota.accesoSin adjunto
dc.pagina.final232
dc.pagina.inicio209
dc.publisherINDIANA UNIV MATH JOURNAL
dc.revistaINDIANA UNIVERSITY MATHEMATICS JOURNAL
dc.rightsregistro bibliográfico
dc.subjectnonlocal diffusion
dc.subjectsign changing solution
dc.subjectuniqueness
dc.subjectASYMPTOTIC-BEHAVIOR
dc.subjectDIRICHLET PROBLEM
dc.subjectTRAVELING-WAVES
dc.subjectEQUATION
dc.subjectUNIQUENESS
dc.subjectEXISTENCE
dc.subjectMODEL
dc.subjectDISPERSAL
dc.subject.ods03 Good Health and Well-being
dc.subject.odspa03 Salud y bienestar
dc.titleStationary Sign Changing Solutions for an Inhomogeneous Nonlocal Problem
dc.typeartículo
dc.volumen60
sipa.codpersvinculados99550
sipa.codpersvinculados99097
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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