Multiple mixed states of nodal solutions for nonlinear Schrödinger systems

  • Jiaquan Liu
  • Xiangqing Liu
  • Zhi-qiang WangEmail author


In this paper we develop a general critical point theory to deal with existence and locations of multiple critical points produced by minimax methods in relation to multiple invariant sets of the associated gradient flow. The motivation is to study non-trivial nodal solutions with each component sign-changing for a class of nonlinear Schrödinger systems which arise from Bose–Einstein condensates theory. Our general method allows us to obtain infinitely many mixed states of nodal solutions for the repulsive case.

Mathematics Subject Classification

35A15 35J50 35J57 58J70 



The authors are grateful to the referee for a careful reading of the manuscript, clarifying some details and pointing out some references. J. Liu is supported by NSFC11171171 and 11271331, X. Liu is supported by NSFC11361077 and Young scholars program of Southwest Associated University, and Z.-Q. Wang is supported by NSFC11271201.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.LMAM, School of Mathematical SciencePeking UniversityBeijingPeople’s Republic of China
  2. 2.Department of MathematicsYunnan Normal UniversityKunmingPeople’s Republic of China
  3. 3.Chern Institute of Mathematics and LPMCNankai UniversityTianjinPeople’s Republic of China
  4. 4.Department of MathematicsUtah State UniversityLoganUSA

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