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In this paper, we study the existence and nonexistence of multiple positive solutions for the inhomogeneous Neumann boundary value problem Δu+up−λu=0, with Dγu=ϕ(x), (*) under some assumptions on the boundary ∂Ω and the function ϕ(x). For ϕ(x)≥0, ϕ(x) 0, ϕ(x) ∈Cα( ), it is shown that there exists a constant λ*＞0 such that problem (*) possesses at least two positive solutions if λ∈ (λ*,∞) and at least one positive solution if λ=λ*. Furthermore, there are no positive solutions for problem (*) if λ∈ (-∞, λ*).

Neumann problem， Positive solution， Supersolution and subsolution

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2010年02月26日

【期刊论文】The asymptotic behaviour of the ground state solutions for Hénon equation

彭双阶， Daomin Cao a， * and Shuangjie Peng a， b

J. Math. Anal. Appl. 278(2003)1-17，-0001，（）：

-1年11月30日

摘要

The main purpose of this paper is to analyze the asymptotic behaviour of the ground state solution of Hénon equation −Δu=|x|αup−1 in Ω, u=0 on ∂Ω (Ω Rn is a ball centered at the origin). It proved that for p close to 2*= 2n/(n−2) (n≥3), the ground state solution up has a unique maximum point xp and dist(xp, ∂Ω)→0 as p→2*. The asymptotic behaviour of up is also given, which deduces that the ground state solution is non-radial.

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华中师范大学，湖北

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