Acta mathematica scientia,Series A ›› 2009, Vol. 29 ›› Issue (5): 1398-1414.

• Articles • Previous Articles     Next Articles

Neumann Problem for Coupled Nonlinear Schrödinger Equations

  

  1. Tin Ka-Ping College of Science, University of Shanghai |for |Science and Technology, Shanghai 200093
  • Received:2007-12-18 Revised:2009-05-27 Online:2009-10-25 Published:2009-10-25
  • Supported by:

    上海市优秀青年教师科研专项基金资助

Abstract:

In this paper, we consider  existence and concentration phenomena of least energy solutions of coupled  nonlinear Schrödinger systems  with Neumann boundary conditions. The focus  is on  the locations of  peaks (maximum points) of the least energy solutions. Following  Tai-Chia Lin and Juncheng Wei's procedure  for  Dirichlet  problem,  least energy solutions for Neumann problem are obtained. As the small perturbed parameter goes to zero, we prove that the peaks of the least energy solutions  approach to the boundary of domain and the energy concentrates around these peaks. On the other hand, peaks of  the two states attract or repulse each other
depending on the interaction between them  to be   attractive or repulsive.

Key words: Concentration of least energy solutions, Nehari manifold, Mountain pass theorem, Coupled nonlinear Schrödinger system

CLC Number: 

  • 35B25
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