Cao, Daomin; Peng, Shuangjie; Yan, Shusen

Author(s)

Cao, Daomin

Peng, Shuangjie

Yan, Shusen

Publication Date

2009

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.

Citation

IMA Journal of Applied Mathematics, 74(3), p. 468-480

ISSN

1464-3634

0272-4960

Link

https://hdl.handle.net/1959.11/5948

Publisher

Oxford University Press

Title

Asymptotic behaviour of ground state solutions for the Hénon equation

Type of document

Journal Article

Entity Type

Publication

Author(s)	Cao, Daomin Peng, Shuangjie Yan, Shusen
Publication Date	2009
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.
Citation	IMA Journal of Applied Mathematics, 74(3), p. 468-480
ISSN	1464-3634 0272-4960
Link	https://hdl.handle.net/1959.11/5948
Publisher	Oxford University Press
Title	Asymptotic behaviour of ground state solutions for the Hénon equation
Type of document	Journal Article
Entity Type	Publication

Asymptotic behaviour of ground state solutions for the Hénon equation

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