Positive supersolutions of non-autonomous quasilinear elliptic equations with mixed reaction

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dc.contributor.authorAghajani, Asodallahcs
dc.contributor.authorRadulescu, Vicentiucs
dc.coverage.issue6cs
dc.coverage.volume73cs
dc.date.accessioned2024-02-20T10:45:38Z
dc.date.available2024-02-20T10:45:38Z
dc.date.issued2023-10-27cs
dc.description.abstractWe provide a simple method for obtaining new Liouville-type theorems for positive supersolutions of the We We provide a simple method for obtaining new Liouville-type theorems for positive supersolutions of the elliptic problem - Delta(p)u+ b(x)vertical bar del u vertical bar(pq/q+1) = c(x)u(q) in Omega, where Omega is an exterior domain in R-N with N >= p > 1 and q >= p - 1. In the case q not equal p - 1, we mainly deal with potentials of the type b(x) = vertical bar x vertical bar(a), c(x) = lambda vertical bar x vertical bar(sigma), where lambda > 0 and a, sigma is an element of R. We show that positive supersolutions do not exist in some ranges of the parameters p, q, a, sigma, which turn out to be optimal. When q = p - 1, we consider the above problem with general weights b(x) >= 0, c(x) > 0 and we assume that c(x)- b(p)(x)/p(p) > 0 for large vertical bar x vertical bar, but we also allow the case lim(vertical bar x vertical bar ->infinity)[c(x)- b(p)(x)/p(p)] = 0. The weights b and c are allowed to be unbounded. We prove that if this equation has a positive supersolution, then the potentials must satisfy a related differential inequality not depending on the supersolution. We also establish sufficient conditions for the nonexistence of positive supersolutions in relationship with the values of tau := lim sup(vertical bar x vertical bar ->infinity) vertical bar x vertical bar b(x) <= infinity. A key ingredient in the proofs is a generalized Hardy-type inequality associated to the p-Laplace operator.en
dc.formattextcs
dc.format.extent2543-2566cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationANNALES DE L INSTITUT FOURIER. 2023, vol. 73, issue 6, p. 2543-2566.en
dc.identifier.doi10.5802/aif.3576cs
dc.identifier.issn1777-5310cs
dc.identifier.orcid0000-0003-4615-5537cs
dc.identifier.other187372cs
dc.identifier.researcheridA-1503-2012cs
dc.identifier.scopus35608668800cs
dc.identifier.urihttps://hdl.handle.net/11012/245083
dc.language.isoencs
dc.publisherAssociation des Annales de l'Institut Fouriercs
dc.relation.ispartofANNALES DE L INSTITUT FOURIERcs
dc.relation.urihttps://aif.centre-mersenne.org/articles/10.5802/aif.3576/cs
dc.rightsCreative Commons Attribution-NoDerivatives 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/1777-5310/cs
dc.rights.urihttp://creativecommons.org/licenses/by-nd/4.0/cs
dc.subjectNonlinear elliptic equationen
dc.subjectLiouville theoremen
dc.subjectsuper solutionen
dc.subjectconvection termen
dc.titlePositive supersolutions of non-autonomous quasilinear elliptic equations with mixed reactionen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-187372en
sync.item.dbtypeVAVen
sync.item.insts2024.02.20 11:45:38en
sync.item.modts2024.02.20 11:12:59en
thesis.grantorVysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií. Ústav matematikycs
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