An infinite dimensional Morse theory
Authors: Wojciech Kryszewski and Andrzej Szulkin
Journal: Trans. Amer. Math. Soc. 349 (1997), 3181-3234
MSC (1991): Primary 58E05; Secondary 34C25, 35J65, 35L05, 55N20, 58F05
MathSciNet review: 1422612
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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.
Keywords: Filtration, cohomology, critical group, Morse inequalities, Morse index, degree theory, Hamiltonian system, wave equation, system of elliptic partial differential equations
Received by editor(s): March 20, 1995
Additional Notes: The first author was supported in part by the KBN Grant PB 513/2/91.
The second author was supported in part by the Swedish Natural Science Research Council.
Article copyright: © Copyright 1997 American Mathematical Society