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.
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This research was supported in part by the Army Research Office under contract # DAAL03-86-K-0074, the Air Force Office of Scientific Research under contract # AF: OSR-84-0376, and the National Science Foundation under contract # DMS-8507056.
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Hale, J.K., Sakamoto, K. Existence and stability of transition layers. Japan J. Appl. Math. 5, 367–405 (1988). https://doi.org/10.1007/BF03167908
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DOI: https://doi.org/10.1007/BF03167908