Abstract
The invention of modern topology goes back to Poincaré, who was led to it in his study of the differential equations of celestial mechanics. Its development was taken over, for quite a while, by people who interestingly enough, seemed to have completely forgotten its origins. Perhaps this really was necessary in order that the subject develop rapidly. In any case, already in the twenties and thirties, people like Morse, Leray, Schauder, and others, were applying topological methods to differential equations. It is our purpose here to explain the relevance of some of these techniques to nonlinear differential equations.
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© 1983 Springer-Verlag New York Inc.
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Smoller, J. (1983). Topological Methods. In: Shock Waves and Reaction—Diffusion Equations. Grundlehren der mathematischen Wissenschaften, vol 258. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-0152-3_12
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DOI: https://doi.org/10.1007/978-1-4684-0152-3_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-0154-7
Online ISBN: 978-1-4684-0152-3
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