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Journal of Dynamics and Differential Equations

, Volume 6, Issue 4, pp 613–629 | Cite as

Bifurcation and stability of stationary solutions of nonlocal scalar reaction-diffusion equations

  • Pedro Freitas
Article

Abstract

The stability of stationary solutions of nonlocal reaction-diffusion equations on a bounded intervalJ of the real line with homogeneous Dirichlet boundary conditions is studied. It is shown that it is possible to have stable stationary solutions which change sign once onJ in the case of constant diffusion when the reaction term does not depend explicitly on the space variable. The problem of the possible types of stable solutions that may exist is considered. It is also shown that Matano's result on the lap-number is still true in the case of nonlocal problems.

Key words

nonlocal reaction-diffusion equations stationary solutions bifurcation from simple eigenvalues 

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Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Pedro Freitas
    • 1
  1. 1.Department of MathematicsHeriot-Watt UniversityEdinburghScotland

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