期刊论文

Peng, Shuangjie（彭双阶）

英文

IMA JOURNAL OF APPLIED MATHEMATICS

0272-4960

2009

74

3

468-480

10.1093/imamat/hxn035

National Natural Science Foundation of China (10631030 to D.C. and S.P.); Science Fund for Creative Research Groups of National Natural Science Foundation of China (10721101) and Chinese Academy of Sciences (KJCX3-SYW-S03) to D.C.; Program for New Century Excellent Talents in University (No.07-0350), the Key Project of Chinese Ministry of Education (No.107081), the Project-sponsored by the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry to S.P.; Australian Research Council of Australia to S.Y.

本校为通讯机构

Let B1(0) ⊂ 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 - Δ u = x αup-1 in B1(0), u = 0 on ∂ B1(0). We prove that for fixed p ∈ (2, 2*), (2* = 2 N/(N - 2)), the maximum point xα of the ground state solution uα satisfies α(1 - xα ) → l ∈ (0,+ ∞) as α → ∞. We also obtain the asymptotic behaviour of uα, which shows that the ground state solution is non-radial. Moreover, we prove the existence of multi-peaked solutions and give their asy...