Acta mathematica scientia,Series B ›› 2012, Vol. 32 ›› Issue (4): 1559-1570.doi: 10.1016/S0252-9602(12)60123-4

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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).

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

CLC Number: 

  • 34C37
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