Acta mathematica scientia,Series B ›› 2009, Vol. 29 ›› Issue (5): 1323-1340.doi: 10.1016/S0252-9602(09)60106-5

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MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER EQUATION WITH MAGNETIC FIELD

PENG Chao-Quan, YANG Jian-Fu   

  1. College of Computer, |South-Central University for Nationalities, Wuhan 430074, China Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China
  • Received:2007-04-24 Online:2009-09-20 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)

Abstract:

The authors consider the semilinear Schrödinger equation
Au+ 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

CLC Number: 

  • 35J60
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