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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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2010年02月26日

【期刊论文】A GLOBAL COMPACTNESS RESULT FOR SINGULAR ELLIPTIC PROBLEMS INVOLVING CRITICAL SOBOLEV EXPONENT

彭双阶， DAOMIN CAO AND SHUANGJIE PENG

Volume 131, Number 6, Pages 1857-1866，-0001，（）：

-1年11月30日

摘要

Let Ω RN be a bounded domain such that 0∈Ω,N≥3, 2*=2N/N-2,λ∈R, ∈∈R. Let {un} H10(Ω) be a (P.S.) sequence of the functional Eλ, ∈(u)=1/2 ƒΩ(|▽u|2-λu2/|x|2-∈u2)-1/2* ƒΩ|u|2*. We study the limit behaviour of un and obtain a global compactness result.

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2010年02月26日

【期刊论文】Semiclassical symmetric Schrödinger equations: existence of solutions concentrating simultaneously on several spheres

彭双阶， Thomas Bartsch， Shuangjie Peng*

，-0001，（）：

-1年11月30日

摘要

We study the radially symmetric Schrödinger equation-ε2△u+V(|x|)u=W(|x|)up, u>0, u∈H1(RN), with N≥1, ε>0 and p>1. As ε→0, we prove the existence of positive radially symmetric solutions concentrating simultaneously on k spheres. The radii are localized near non-degenerate critical points of the function Γ(r)=rN−1[V(r)]p+1/p−1−1/2[W(r)]−2/p−1.

nonlinear Schrödinger equation,， radial solutions,， spike-layer solutions,， multi-peak solutions,， variational methods.，