Acta mathematica scientia, Series B >
NODAL BOUND STATES WITH CLUSTERED SPIKES FOR NONLINEAR SCHRÖDINGER EQUATIONS
Received date: 2013-04-24
Revised date: 2014-05-15
Online 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).
We consider the following nonlinear Schr¨odinger equations −"2Δu + u = Q(x)|u|p−2u in RN, u ∈ H1(RN), 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+.
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 . DOI: 10.1016/S0252-9602(14)60133-8
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