Existence and stability of transition layers

  • Jack K. Hale
  • Kunimochi Sakamoto

DOI: 10.1007/BF03167908

Cite this article as:
Hale, J.K. & Sakamoto, K. Japan J. Appl. Math. (1988) 5: 367. doi:10.1007/BF03167908


For a second order nonautonomous singularly perturbed ordinary differential equation with Neumann boundary conditions, the existence of single transition layer solutions is proved by using the method of Liapunov-Schmidt. The method also gives the stability of these solutions as an equilibrium point of a parabolic equation.

Key words

singular perturbation transition layers dynamical systems Liapunov-Schmidt 

Copyright information

© JJAM Publishing Committee 1988

Authors and Affiliations

  • Jack K. Hale
    • 1
  • Kunimochi Sakamoto
    • 1
  1. 1.Lefschetz Center for Dynamical Systems, Division of Applied MathematicsBrown UniversityProvidence

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