Acta mathematica scientia, Series B >
MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER EQUATION WITH MAGNETIC FIELD
Received date: 2007-04-24
Online published: 2009-09-20
Supported by
The first author was supported by NSF of South-Central University for Nationalities (yzz08001) and the second author was supported by NNSF of China (10571175 and 10631030)
The authors consider the semilinear Schrödinger equation
-ΔAu+ Vλ(x)u=Q(x)|u|γ-2 u in RN,
where 1< γ < 2* and γ≠ 2, Vλ = V+ - λV-. Exploiting the relation between the Nehari manifold and fibrering maps, the existence of nontrivial solutions for the problem is discussed.
Key words： Nehari manifold; fibrering maps; Schrödinger equation
PENG Chao-Quan , YANG Jian-Fu . MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER EQUATION WITH MAGNETIC FIELD[J]. Acta mathematica scientia, Series B, 2009 , 29(5) : 1323 -1340 . DOI: 10.1016/S0252-9602(09)60106-5
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