Abstract
Systems of singularly perturbed ordinary differential equations can often be solved approximately by singular solutions. These singular solutions are pieced together from solutions to simpler sets of equations obtained as limits from the original equations. There is a large body of literature on the question of when the existence of a singular solution implies the existence of an actual solution to the original equations. Techniques that have been used include fixed point arguments (Conley [1], Carpenter [2], Hastings [3] and Gardner and Smoller [4]), implicit function theorem and related functional-analytic techniques (Fife [5], Fujii et al. [6], Hale and Sakamoto [7,8]) differential inequalities (see for instance Chang and Howes [9]) and nonstandard analysis (Diener and Reeb [10]).
Research partially supported by NSF DMS 880 1627 and an award from the Graduate Research Board of the University of Maryland
Research partially supported by NSF DMS 8901913 and AFOSR-90–0017
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Jones, C., Kopell, N., Langer, R. (1991). Construction of the Fitzhugh-Nagumo Pulse Using Differential Forms. In: Aris, R., Aronson, D.G., Swinney, H.L. (eds) Patterns and Dynamics in Reactive Media. The IMA Volumes in Mathematics and its Applications, vol 37. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3206-3_7
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