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The asymptotic behavior of the ground state solutions for biharmonic equations

✍ Scribed by Yajing Zhang; Jianghao Hao

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 243 KB
Volume: 74
Category: Article
ISSN: 0362-546X
DOI: 10.1016/j.na.2010.12.027

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✦ Synopsis

In this paper we study the asymptotic behavior of the ground state solutions of the Hénon type biharmonic equation ∆ 2 u = |x| α u p-1 in Ω, u > 0 in Ω and u = ∂u ∂n = 0 on ∂Ω, where Ω is the unit ball in R N , α > 0, p > 2. We prove that the ground state solution u p concentrates on a boundary point and has a unique maximum point as p → 2 * = 2N

N-4 , which deduce that the ground state solution u p is not radially symmetric.

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