期刊论文

Peng, Shuangjie

英文

Communications in Partial Differential Equations

0360-5302

2009

34

12

1566-1591

10.1080/03605300903346721

Both D. Cao and S. Peng were supported by the Key Project of NSFC (No. 10631030). D. Cao was also supported partially by Science Fund for Creative Research Groups of Natural Science Foundation of China (No. 10721101). S. Peng was also supported by the Program for New Century Excellent Talents in University (No. 07-0350) and the Key Project of Chinese Ministry of Education (107081).

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In this paper we study the existence and qualitative property of standing wave solutions for the nonlinear Schrödinger equation . Let . For any integer k ≥ 1, we prove existence of standing wave solutions with u > 0 having k local maximum points and concentrating near a given local maximum point of Γ when ε is small. The potentials V and K are allowed to be either vanishing or unbounded at infinity. Existence of solutions concentrating near k distinct non-degenerate critical points of Γ has...