Journal of Dynamics and Differential Equations

, Volume 31, Issue 3, pp 1653–1670 | Cite as

Existence of Pulses for the System of Competition of Species

  • Martine MarionEmail author
  • Vitaly Volpert


The paper is concerned with the existence of pulses for monotone reaction–diffusion systems of two equations. For a general class of systems we prove that pulses exist if and only if the wave solutions propagate at positive speed. This result is applied to investigate the existence of pulses for the system of competition of species.


Existence of pulses Monotone systems Leray–Schauder method 

Mathematics Subject Classification

35K57 47F05 



The second author was partially supported by the Ministry of Education and Science of the Russian Federation (the Agreement Number 02.a03.21.0008) and by the program PICS CNRS 6583 Matbio.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institut Camille Jordan, UMR 5585 CNRSEcole Centrale de LyonEcullyFrance
  2. 2.Institut Camille Jordan, UMR 5585 CNRSUniversity Lyon 1VilleurbanneFrance
  3. 3.RUDN UniversityMoscowRussia

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