Competition in Periodic Media: III—Existence and Stability of Segregated Periodic Coexistence States

  • Léo GirardinEmail author
  • Alessandro Zilio


In this paper we consider a system of parabolic reaction–diffusion equations with strong competition and two related scalar reaction–diffusion equations. We show that in certain space periodic media with large periods, there exist periodic, non-constant, non-trivial, stable stationary states. We compare our results with already known results about the existence and nonexistence of such solutions. Finally, we provide ecological interpretations for these results.


Competition–diffusion system Periodic media Segregation Stability 

Mathematics Subject Classification

35B10 35B35 35B40 35K57 92D25 



The authors thank Grégoire Nadin for the attention he paid to this work and Cécile Carrère and Henri Berestycki for pointing out the interest of this problem.


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Authors and Affiliations

  1. 1.Laboratoire Jacques-Louis Lions, CNRS UMR 7598Université Pierre et Marie CurieParisFrance
  2. 2.Laboratoire Jacques-Louis Lions, CNRS UMR 7598Université Paris DiderotParisFrance

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