数学物理学报（英文版）
數學物理學報（英文版）
수학물이학보（영문판）
ACTA MATHEMATICA SCIENTIA
2014年
6期
1882-1896
,共15页
nodal bound states%Lyapunov-Schmidt reduction%Schr¨odinger equations
We consider the following nonlinear Schr¨odinger equations?ε2?u+u=Q(x)|u|p?2u in RN, u∈H1(RN), where ε is a small positive parameter, N ≥ 2, 2 < p < ∞ for N = 2 and 2 < p < 2NN?2 for N ≥ 3. We prove that this problem has sign-changing (nodal) semi-classical bound states with clustered spikes for su?ciently smallεunder some additional conditions on Q(x). Moreover, the number of this type of solutions will go to infinity asε→0+.
