数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1559-1570.doi: 10.1016/S0252-9602(12)60123-4

• 论文 • 上一篇    下一篇

EXISTENCE OF SOLUTIONS FOR NON-PERIODIC SUPERLINEAR SCHRÖDINGER EQUATIONS WITHOUT (AR) CONDITION

万莉莉1,2, 唐春雷1   

  1. 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
    2. School of Science, Southwest University of Science and Technology, Mianyang 621010, China
  • 收稿日期:2010-06-07 修回日期:2011-07-05 出版日期:2012-07-20 发布日期:2012-07-20
  • 基金资助:

    Supported by National Natural Science Foundation of China (11071198) and Doctor Research Foundation of Southwest University of Science and Technology (11zx7130), the Key Project in Science and Technology Research Plan of the Education Department of Hubei Province (D20112605).

EXISTENCE OF SOLUTIONS FOR NON-PERIODIC SUPERLINEAR SCHRÖDINGER EQUATIONS WITHOUT (AR) CONDITION

 WAN Li-Li1,2, TANG Chun-Lei1   

  1. 1. School of Mathematics and Statistics, Southwest University, Chongqing 400715, China;
    2. School of Science, Southwest University of Science and Technology, Mianyang 621010, China
  • Received:2010-06-07 Revised:2011-07-05 Online:2012-07-20 Published:2012-07-20
  • Supported by:

    Supported by National Natural Science Foundation of China (11071198) and Doctor Research Foundation of Southwest University of Science and Technology (11zx7130), the Key Project in Science and Technology Research Plan of the Education Department of Hubei Province (D20112605).

摘要:

The existence of solutions is obtained for a class of the non-periodic Schr¨odinger equation −Δu + V (x)u = f(x, u), RN, by the generalized mountain pass theorem, where V is large at infinity and f is superlinear as |u| →∞.

关键词: Schr¨odinger equation, superlinear, generalized mountain pass theorem

Abstract:

The existence of solutions is obtained for a class of the non-periodic Schr¨odinger equation −Δu + V (x)u = f(x, u), RN, by the generalized mountain pass theorem, where V is large at infinity and f is superlinear as |u| →∞.

Key words: Schr¨odinger equation, superlinear, generalized mountain pass theorem

中图分类号: 

  • 34C37