On the uniqueness of positive solutions of a quasilinear equation containing a weighted p-Laplacian, the superlinear case

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dc.contributor.authorGarcia Huidobro, Marta
dc.contributor.authorHenao, Duvan A.
dc.date.accessioned2024-01-10T12:07:11Z
dc.date.available2024-01-10T12:07:11Z
dc.date.issued2008
dc.description.abstractWe consider the quasilinear equation of the form
dc.description.abstract-Delta(p)u = K(vertical bar x vertical bar) f(u), x epsilon R-n, n > p > 1, (P)
dc.description.abstractwhere Delta(p)u := div(|del u|(p- 2)del u) is the degenerate p-Laplace operator and the weight K is a positive C-1 function defined in R+. We deal with the case in which f epsilon C[0, infinity) has one zero at u(0) > 0, is non positive and not identically 0 in (0, u(0)), and is locally Lipschitz, positive and satisfies some superlinear growth assumption in (u(0), infinity). We carefully study the behavior of the solution of the corresponding initial value problem for the radial version of the quasilinear equation, as well as the behavior of its derivative with respect to the initial value. Combining, as Cortazar, Felmer and Elgueta, comparison arguments due to Coffman and Kwong, with some separation results, we show that any zero of the solutions of the initial value problem is monotone decreasing with respect to the initial value, which leads immediately the uniqueness of positive radial ground states, and the uniqueness of positive radial solutions of the Dirichlet problem on a ball.
dc.fechaingreso.objetodigital2024-05-13
dc.format.extent28 páginas
dc.fuente.origenWOS
dc.identifier.doi10.1142/S0219199708002831
dc.identifier.eissn1793-6683
dc.identifier.issn0219-1997
dc.identifier.urihttps://doi.org/10.1142/S0219199708002831
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/76254
dc.identifier.wosidWOS:000256544600005
dc.information.autorucMatemática;García-Huidobro M;S/I;60600
dc.information.autorucMatemática;Henao D;S/I;127635
dc.issue.numero3
dc.language.isoen
dc.nota.accesoSin adjunto
dc.pagina.final432
dc.pagina.inicio405
dc.publisherWORLD SCIENTIFIC PUBL CO PTE LTD
dc.revistaCOMMUNICATIONS IN CONTEMPORARY MATHEMATICS
dc.rightsregistro bibliográfico
dc.subjectpositive solutions
dc.subjectuniqueness
dc.subjectsuperlinear
dc.subjectseparation
dc.subjectSEMILINEAR ELLIPTIC-EQUATIONS
dc.subjectGROUND-STATE SOLUTIONS
dc.subjectRADIAL SOLUTIONS
dc.subjectNONNEGATIVE SOLUTIONS
dc.subjectASYMPTOTIC-BEHAVIOR
dc.subjectRN
dc.subjectDELTA-U+F(U)=0
dc.subjectEXISTENCE
dc.subjectR(N)
dc.subjectSYMMETRY
dc.titleOn the uniqueness of positive solutions of a quasilinear equation containing a weighted p-Laplacian, the superlinear case
dc.typeartículo
dc.volumen10
sipa.codpersvinculados60600
sipa.codpersvinculados127635
sipa.indexWOS
sipa.indexScopus
sipa.trazabilidadCarga SIPA;09-01-2024
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