NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRÖDINGER EQUATIONS

doi:10.1016/S0252-9602(14)60133-8

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (6): 1892-1906.doi: 10.1016/S0252-9602(14)60133-8

NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRÖDINGER EQUATIONS

代晋军, 何其汉, 李必文

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China； School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

收稿日期:2013-04-24 修回日期:2014-05-15 出版日期:2014-11-20 发布日期:2014-11-20
基金资助:
He was supported by NSFC (11301204); Li was supported by program for outstanding young Technology Innovative team in universities of Hubei Province (T2014212).

NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRÖDINGER EQUATIONS

DAI Jin-Jun, HE Ji-Han, LI Bi-Wen

School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China； School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China

Received:2013-04-24 Revised:2014-05-15 Online:2014-11-20 Published:2014-11-20
Supported by:
He was supported by NSFC (11301204); Li was supported by program for outstanding young Technology Innovative team in universities of Hubei Province (T2014212).

摘要/Abstract

摘要：

We consider the following nonlinear Schr¨odinger equations −"2Δu + u = Q(x)|u|^p−2u in R^N, u ∈ H¹(R^N), where " is a small positive parameter, N ∈ 2, 2 < p < 1 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 " under some additional conditions on Q(x). Moreover, the number of this type of solutions will go to infinity as ε→ 0⁺.

关键词: nodal bound states, Lyapunov-Schmidt reduction, Schr¨odinger equations

Abstract:

Key words: nodal bound states, Lyapunov-Schmidt reduction, Schr¨odinger equations

中图分类号:

35J10

代晋军, 何其汉, 李必文. NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRÖDINGER EQUATIONS[J]. 数学物理学报(英文版), 2014, 34(6): 1892-1906.

DAI Jin-Jun, HE Ji-Han, LI Bi-Wen. NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRÖDINGER EQUATIONS[J]. Acta mathematica scientia,Series B, 2014, 34(6): 1892-1906.

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NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRÖDINGER EQUATIONS

NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRÖDINGER EQUATIONS

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