Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (1): 65-79.

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Mountain Pass Solutions for Fractional Coupled Nonlinear Schrödinger Systems

Wei Gongming, Li qing   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093
  • Received:2015-08-03 Revised:2015-12-23 Online:2016-02-25 Published:2016-02-25
  • Supported by:

    Supported by the NSFC (11471215) and Hujiang Foundation of China (B14005)

Abstract:

In this paper, we study the existence of nontrivial solutions for fractional coupled nonlinear Schrödinger systems with Dirichlet boundary conditions. Our method is to use Mountain Pass Theorem in fractional order Sobolev spaces. The main points are to prove that the PS condition is satisfied and the mountain pass solution for the system is actually nontrivial.

Key words: Fractional Laplace operator, Critical point, Mountain Pass Theorem, Palais-Smale condition, Least energy solution

CLC Number: 

  • O175.2
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