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On an elliptic attractor in an asymptotically symmetric unbounded domain in ℝ + 4
Author(s) -
Efendiev M.
Publication year - 2007
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/blms/bdm082
Subject(s) - symmetrization , mathematics , attractor , conjecture , domain (mathematical analysis) , pure mathematics , mathematical analysis
We study the positive solutions of a semilinear elliptic problem in an asymptotically symmetric unbounded domain Ω + in ℝ 4 . The existence of the global attractor for the trajectory dynamical system associated with this problem is proved. Based on the recent development of the De Giorgi conjecture, the symmetrization and stabilization properties of positive solutions as | x |→∞ are also established in the four‐dimensional case.