Article

Japan Journal of Applied Mathematics

, Volume 5, Issue 3, pp 367-405

First online:

Existence and stability of transition layers

  • Jack K. HaleAffiliated withLefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University
  • , Kunimochi SakamotoAffiliated withLefschetz Center for Dynamical Systems, Division of Applied Mathematics, Brown University

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Abstract

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