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General Uniqueness Results and Variation Speed for Blow-Up Solutions of Elliptic Equations

Authors:	Cirstea, Florica Corina Du, Yihong

Affiliation:	School of Computer Science and Mathematics, Victoria University of Technology PO Box 14428, Melbourne, VIC 8001, Australia School of Mathematics, Statistics and Computer Science, University of New England Armidale, NSW 2351, Australia and Department of Mathematics, Qufu Normal University P.R. China. E-mail: ydu{at}turing.une.edu.au, http://mcs.une.edu.au/~ydu/

Abstract:	Let ${Omega}$ be a smooth bounded domain in R^N. We prove general uniquenessresults for equations of the form ${Delta}$ u = au b(x)f(u) in ${Omega}$ , subject to u = ${infty}$ on ${partial}$ ${Omega}$ . Our uniqueness theorem is establishedin a setting involving Karamata's theory on regularly varyingfunctions, which is used to relate the blow-up behavior of u(x)with f(u) and b(x), where b ${equiv}$ 0 on ${partial}$ ${Omega}$ and a certain ratio involvingb is bounded near ${partial}$ ${Omega}$ . A key step in our proof of uniqueness usesa modification of an iteration technique due to Safonov. 2000Mathematics Subject Classification 35J25 (primary), 35B40, 35J60(secondary).

Keywords:	boundary blow-up elliptic equation regularly varying functions
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