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General Uniqueness Results and Variation Speed for Blow‐Up Solutions of Elliptic Equations
Author(s) -
Cîrstea Florica Corina,
Du Yihong
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611505015273
Subject(s) - uniqueness , mathematics , bounded function , mathematics subject classification , domain (mathematical analysis) , uniqueness theorem for poisson's equation , pure mathematics , subject (documents) , key (lock) , mathematical analysis , ecology , library science , computer science , biology
Let Ω be a smooth bounded domain in R N . We prove general uniqueness results for equations of the form − Δ u = au − b ( x ) f ( u ) in Ω, subject to u = ∞ on ∂ Ω . Our uniqueness theorem is established in a setting involving Karamata's theory on regularly varying functions, which is used to relate the blow‐up behavior of u ( x ) with f ( u ) and b ( x ), where b ≡ 0 on ∂ Ω and a certain ratio involving b is bounded near ∂ Ω. A key step in our proof of uniqueness uses a modification of an iteration technique due to Safonov. 2000 Mathematics Subject Classification 35J25 (primary), 35B40, 35J60 (secondary).