2016, 2007, English, Article, Journal or magazine article edition: Boundary blow-up in nonlinear elliptic equations of Bieberbach--Rademacher type Cîrstea, Florica-Corina; Rădulescu, Vicenţiu

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Bookmark: http://trove.nla.gov.au/version/225316913
Physical Description
  • journal article
Published
  • American Mathematical Society, 2016-03-15T22:37:57Z 2007-02-13 2016-06-14T08:38:45Z
Language
  • English

Edition details

Title
  • Boundary blow-up in nonlinear elliptic equations of Bieberbach--Rademacher type
Author
  • Cîrstea, Florica-Corina
  • Rădulescu, Vicenţiu
Published
  • American Mathematical Society, 2016-03-15T22:37:57Z 2007-02-13 2016-06-14T08:38:45Z
Physical Description
  • journal article
Part Of
  • Transactions of the American Mathematical Society
Subjects
Summary
  • We establish the uniqueness of the positive solution for equations of the form −∆u =​ au − b(x)f(u) in Ω, u|∂Ω =​ ∞. The special feature is to consider nonlinearities f whose variation at infinity is not regular (e.g., exp(u) − 1, sinh(u), cosh(u) − 1, exp(u) log(u + 1), uᵝ exp(uᵞ), β ∈ R, γ > 0 or exp(exp(u)) − e) and functions b ≥ 0 in Ω vanishing on ∂Ω. The main innovation consists of using Karamata’s theory not only in the statement/​proof of the main result but also to link the nonregular variation of f at infinity with the blow-up rate of the solution near ∂Ω.
  • The research of the first author was carried out at Victoria University (Melbourne) with the support of the Australian Government through DETYA. The second author has been supported by Grant 2-CEX06-11-18/​2006.
Terms of Use
  • © 2007 American Mathematical Society
Language
  • English
Identifier
  • oai:openresearch-repository.anu.edu.au:1885/​100254
  • 10.1090/​S0002-9947-07-04107-4
  • oai:digitalcollections.anu.edu.au:1885/​100254
  • 0002-9947

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