期刊论文

Peng, Shuangjie（彭双阶）

英文

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE

0294-1449

2010

27

5

1205-1226

10.1016/j.anihpc.2010.05.003

The authors would like to express their sincere gratitude to the referee for a very careful reading of the paper, for all his insightful comments and valuable suggestions. Both Deng and Peng were partially supported by the Key Project of NSFC (No. 10631030). Peng was also partially supported by the program from NCET (No. 07-0350) and self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (CCNU09C01007).

本校为第一且通讯机构

In this paper, we will study the existence and qualitative property of standing waves ε(x,t)=e-iEt/εu(x) for the nonlinear Schrödinger equation iεℓεℓt+ε2/2mΔxε-(V(x)+E) ε+K(x)|ε|p-1ε=0, (t,x)∈R+×RN. Let G(x)=[V(x)]p+1/p-1-N/2×[K(x)]-2/p-1 and suppose that G(x) has k local minimum points. Then, for any l∈{1,...,k}, we prove the existence of the standing waves in H1(RN) having exactly l local maximum points which concentrate near l local minimum points of G(x) respectively as ε→0. The potentials V(x) and K(x) are allowed to be ...