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An approximate Gidas–Ni–Nirenberg theorem
Author(s) -
Rosset Edi
Publication year - 1994
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670171304
Subject(s) - mathematics , nirenberg and matthaei experiment , perturbation (astronomy) , pure mathematics , mathematical analysis , physics , quantum mechanics
We study positive solutions u to Δ u + f ( u ) = 0 in Ω, u = 0 on ∂Ω, and we address the following question: If Ω is a small perturbation of a ball, is u a small perturbation of a radially symmetric function? We prove two theorems which give an affirmative answer under different assumptions on the non‐linearity f and on the topologies in which perturbations are considered.