Origin and evolution of the Palais-Smale condition in critical point theory

Mawhin, Jean;Willem, Michel
(2010) J P Journal of Fixed Point Theory and Applications — Vol. 7, n° 2, p. 265-290 (2010)

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  • Mawhin, JeanUCLouvain
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  • Willem, MichelUCLouvain
    Author
Abstract
In 1963–64, Palais and Smale have introduced a compactness condition, namely condition (C), on real functions of class C 1 defined on a Riemannian manifold modeled upon a Hilbert space, in order to extend Morse theory to this frame and study nonlinear partial differential equations. This condition and some of its variants have been essential in the development of critical point theory on Banach spaces or Banach manifolds, and are referred as Palais–Smale-type conditions. The paper describes their evolution.
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Mawhin, J., & Willem, M. (2010). Origin and evolution of the Palais-Smale condition in critical point theory. J P Journal of Fixed Point Theory and Applications, 7(2), 265-290. https://doi.org/10.1007/s11784-010-0019-7 (Original work published 2010)