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A Critical Phenomenon for Sublinear Elliptic Equations in Cone‐Like Domains
Author(s) -
Kondratiev Vladimir,
Liskevich Vitali,
Moroz Vitaly,
Sobol Zeev
Publication year - 2005
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609305004492
Subject(s) - sublinear function , mathematics , cone (formal languages) , elliptic curve , exponent , mathematical analysis , critical exponent , pure mathematics , geometry , algorithm , philosophy , linguistics , scaling
The authors of this paper study positive supersolutions to the elliptic equation ‐Δ u = c | x | − s u p in Cone‐like domains of R N ( N ⩾ 2), where p, s ∈ R and c > 0. They prove that in the sublinear case p < 1 there exists a critical exponent p * > 1 such that the equation has a positive supersolution if and only if −∞ < p < p * . The value of p * is determined explicitly by s and the geometry of the cone. 2000 Mathematics Subject Classification 35J60 (primary), 35B05, 35R45 (secondary).