Existence of Spikes for the Gierer-Meinhardt System in One Dimension

  • Juncheng Wei
  • Matthias Winter
Part of the Applied Mathematical Sciences book series (AMS, volume 189)


We give a full account of the existence of multiple spikes for the Gierer-Meinhardt system in an interval on the real line. We present a unified rigorous approach based on the Liapunov-Schmidt method which is very flexible and consider the cases of symmetric and asymmetric multi-spike solutions. We also study clustered multiple spikes.


Implicit Function Theorem Multiple Cluster Geometric Singular Perturbation Theory Multiple Spike Order Normal Form 
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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  • Juncheng Wei
    • 1
  • Matthias Winter
    • 2
  1. 1.Department of MathematicsThe Chinese University of Hong KongHong KongChina
  2. 2.Department of Mathematical SciencesBrunel UniversityUxbridgeUK

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