Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00208-003-0468-z
Title: Blow-up solutions of nonlinear elliptic equations in ℝn with critical exponent
Authors: Leung, M.C. 
Keywords: Blow-up solutions
Decay estimates
Nonlinear differential equation
Scalar curvature
Issue Date: Dec-2003
Source: Leung, M.C. (2003-12). Blow-up solutions of nonlinear elliptic equations in ℝn with critical exponent. Mathematische Annalen 327 (4) : 723-744. ScholarBank@NUS Repository. https://doi.org/10.1007/s00208-003-0468-z
Abstract: For an integer n ≥ 3 and any positive number ε, we establish the existence of smooth functions K on ℝn\{0} with |K - 1| ≥ ε, such that the equation Au+n(n-2)Kun+2/n-2 = 0 in ℝ n\{0} has a smooth positive solution which blows up at the origin (i.e., u does not have slow decay near the origin). Furthermore, we show that in some situations K can be extended as a Lipschitz function on ℝ n. These provide counter-examples to a conjecture of C.-S. Lin when n > 4, and a question of Taliaferro.
Source Title: Mathematische Annalen
URI: http://scholarbank.nus.edu.sg/handle/10635/102937
ISSN: 00255831
DOI: 10.1007/s00208-003-0468-z
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