数学物理学报(英文版) ›› 2009, Vol. 29 ›› Issue (5): 1323-1340.doi: 10.1016/S0252-9602(09)60106-5

• 论文 • 上一篇    下一篇

MULTIPLE SOLUTIONS FOR THE SCHRÖDINGER EQUATION WITH MAGNETIC FIELD

彭超权, 杨健夫   

  1. College of Computer, |South-Central University for Nationalities, Wuhan 430074, China Department of Mathematics, Jiangxi Normal University, Nanchang 330022, China
  • 收稿日期:2007-04-24 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:

    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)

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)

摘要:

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.

关键词: Nehari manifold, fibrering maps,  Schrödinger equation

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

中图分类号: 

  • 35J60