Kryszewski, Wojciech; Szulkin, Andrzej An infinite dimensional Morse theory with applications. (English) Zbl 0892.58015 Trans. Am. Math. Soc. 349, No. 8, 3181-3234 (1997). 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. Reviewer: D.Andrica (Cluj-Napoca) Cited in 5 ReviewsCited in 72 Documents 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 Keywords:filtration; cohomology; critical group; Morse inequalities; Morse index; degree theory; Hamiltonian system; wave equation; system of elliptic partial differential equations PDFBibTeX XMLCite \textit{W. Kryszewski} and \textit{A. Szulkin}, Trans. Am. Math. Soc. 349, No. 8, 3181--3234 (1997; Zbl 0892.58015) Full Text: DOI