Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (6): 1035-1044.

• Articles • Previous Articles     Next Articles

The Existence of Nontrivial Solutions for a Class of Asymptotically Linear Equation

 PENG Chao-Quan, MA Shi-Chao   

  1. College of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 430074
  • Received:2012-02-20 Revised:2013-03-08 Online:2013-12-25 Published:2013-12-25
  • Supported by:

    中南民族大学中央高校基本科研业务费专项资金(CZY12013)和中南民族大学大学生创新创业训练计划(GCX12030)资助

Abstract:

In this paper, we show that the nonlinear SchrÖdinger equation
u +V(x)u=f(x, u),  x∈RN
possesses multiple solutions in H1(RN),  where N≥3 and the potential V(x) is a continuous function satisfying V(x)≥V0>0 for all x∈RN, f(x, t) is a continuous function in RNR and asymptotically linear or superlinear at infinity for t.

Key words: Existence, Multiple solutions, SchrÖdinger equation

CLC Number: 

  • 35J60
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