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An infinite dimensional Morse theory with applications. (English) Zbl 0892.58015

In the first sections of this very interesting and long paper, the authors present an infinite dimensional (extraordinary) cohomology theory closely connected to critical point theory: cohomology of filtered spaces, critical groups, Morse inequalities, computation of critical groups, relation to degree theory. In the last part, several applications to Hamiltonian systems, the one-dimensional wave equation of vibrating string type, and systems of elliptic partial differential equations are given. A rich and suggestive bibliography on these topics is also included.

MSC:

58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
34C25 Periodic solutions to ordinary differential equations
35L05 Wave equation
55N20 Generalized (extraordinary) homology and cohomology theories in algebraic topology
37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
35J65 Nonlinear boundary value problems for linear elliptic equations
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