中国科技论文在线

上传时间

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.，

48浏览
0点赞
0收藏
0分享
74下载
0

引用

上传时间

2010年02月26日

【期刊论文】A new type of solutions for a singularly perturbed elliptic Neumann problem

彭双阶， Gongbao Li， Shuangjie Peng and Shusen Yan

Rev. Mat. Iberoamericana 23 (2007), no.3, 1039-1066，-0001，（）：

-1年11月30日

摘要

We prove the existence of positive solutions concentrating simultaneously on some higher dimensional manifolds near and on the boundary of the domain for a nonlinear singularly perturbed elliptic Neumann problem.

Singularly perturbed elliptic equation， variational method,， concentrating solutions,， higher dimensional manifolds.，

20浏览
0点赞
0收藏
0分享
47下载
0

引用

上传时间

2010年02月26日

【期刊论文】CONCENTRATION OF SOLUTIONS FOR A PANEITZ TYPE PROBLEM

彭双阶， Shuangjie Peng， Jing Zhou

DYNAMICAL SYSTEMS Volume 26, Number 3, March 2010 pp. 1055-1072，-0001，（）：

-1年11月30日

摘要

By variational methods, we construct infinitely many concentra-tion solutions for a type of Paneitz problem under the condition that the Paneitz curvature has a sequence of strictly local maximum points moving to infinity.

19浏览
0点赞
0收藏
0分享
47下载
0

引用

上传时间

2010年02月26日

【期刊论文】Sign-changing solutions for elliptic problems with critical Sobolev-Hardy exponents☆

彭双阶， Dongsheng Kang a， ∗ and Shuangjie Peng b

J. Math. Anal. Appl. 291(2004)488-499，-0001，（）：

-1年11月30日

摘要

Let Ω RN be a smooth bounded domain such that 0 ∈Ω, N≥7, 0≤s＜2, 2*(s)=2(N−s)/(N−2). We prove the existence of sign-changing solutions for the singular critical problem −Δu−μ(u/|x|2)=(|u|2∗(s)−2/|x|s)u+λu with Dirichlet boundary condition on Ω for suitable positive parameters λ and μ.

Sign-changing solutions， Compactness， Critical Sobolev-Hardy exponents， Singularity

34浏览
0点赞
0收藏
0分享
43下载
0

引用

上传时间

2010年02月26日

【期刊论文】An elliptic equation with combined critical Sobolev-Hardy terms

彭双阶， Wenliang Gaoa，， Shuangjie Pengb， *

Nonlinear Analysis 65(2006)1595-1612，-0001，（）：

-1年11月30日

摘要

Let Ω be a bounded domain in RN (N≥3) with the origin 0 ∈Ω, μ<((N-2)/2)2, 2*(s)=2(N-s)/(N-2); K(x)≥0 and Q(x)≥0 are two smooth functions on Ω. In this paper, we investigate the singular elliptic equation-△u=μu/|x|2+K(x)u2*(s)−1/|x|s+Q(x)u2*(t)−1/|x−x0|t+f(x,u) with Dirichlet boundary conditions. We study the limit behavior of the (P.S.) sequence of the corresponding energy functional and give a global compactness theorem, and then give some existence results.

Sobolev-Hardy terms， Compactness

25浏览
0点赞
0收藏
0分享
60下载
0

引用