Asymptotic behaviour of ground state solutions for the Hénon equation

Title
Asymptotic behaviour of ground state solutions for the Hénon equation
Publication Date
2009
Author(s)
Cao, Daomin
Peng, Shuangjie
Yan, Shusen
Type of document
Journal Article
Language
en
Entity Type
Publication
Publisher
Oxford University Press
Place of publication
United Kingdom
DOI
10.1093/imamat/hxn035
UNE publication id
une:6092
Abstract
Let B₁(0) 'C RN' be the unit ball centred at the origin, N ≥ 3. In this paper, we analyse the profile of the ground state solution of the Hénon equation - ∆u = │x│'au⁻¹ in B₁ (0), u = 0 on ∂B₁ (0). We prove that for fixed p ε (2,2*), (2* = 2N/(N - 2)), the maximum point xₐ of the ground state solution uₐ satisfies a(1 - │xₐ│) → l ε(0,+ ∞) as a → ∞. We also obtain the asymptotic behaviour of uₐ, which shows that the ground state solution is non-radial. Moreover, we prove the existence of multi-peaked solutions and give their asymptotic behaviour.
Link
Citation
IMA Journal of Applied Mathematics, 74(3), p. 468-480
ISSN
1464-3634
0272-4960
Start page
468
End page
480

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