| NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRDINGER EQUATIONS |
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| 引用本文： | 代晋军,;何其涵,;李必文.NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRDINGER EQUATIONS[J].数学物理学报(B辑英文版),2014(6):1892-1906. |
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| 作者姓名： | 代晋军 ;何其涵 ;李必文 |
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| 基金项目： | supported by NSFC（11301204）; supported by program for outstanding young Technology Innovative team in universities of Hubei Province（T2014212）, Acknowledgements The authors of the paper would like to thank Professor Shuangjie Peng＇for his valuable comment and suggestion. |
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| 摘 要： | 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 2N/N-2 for N ≥ 3. We prove that this problem has sign-changing(nodal) semi-classical bound states with clustered spikes for sufficiently small ε under some additional conditions on Q(x).Moreover, the number of this type of solutions will go to infinity as ε→ 0+.
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| 关 键 词： | 非线性方程 束缚态 薛定谔方程 群集 附加条件 无穷大 |
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