An infinite dimensional Morse theory with applications

Kryszewski, Wojciech; Szulkin, Andrzej

doi:10.1090/S0002-9947-97-01963-6

An infinite dimensional Morse theory with applications
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by Wojciech Kryszewski and Andrzej Szulkin

Trans. Amer. Math. Soc. 349 (1997), 3181-3234

DOI: https://doi.org/10.1090/S0002-9947-97-01963-6

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Abstract:

In this paper we construct an infinite dimensional (extraordinary) cohomology theory and a Morse theory corresponding to it. These theories have some special properties which make them useful in the study of critical points of strongly indefinite functionals (by strongly indefinite we mean a functional unbounded from below and from above on any subspace of finite codimension). Several applications are given to Hamiltonian systems, the one-dimensional wave equation (of vibrating string type) and systems of elliptic partial differential equations.

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