Abstract
In Morse theory the behavior of a C2Euler functionalF, defined on a Hilbert spaceH,near its critical points can be described by the estimates of thecritical groupsin the critical points. For convenience of the reader we recall the definition of critical group. For any a e R, we denote. Moreover let u be a critical point ofF, at levelc = F(u).We call the qth critical group ofFat u,q =0, 1, 2,…, whereHq (A,B)stands for the qth Alexander-Spanier cohomology group of the pair (A,B)with coefficients in 1K (cf. [2]).
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Cingolani, S., Vannella, G. (2003). Morse Index Computations for a Class of Functionals Defined in Banach Spaces. In: Lupo, D., Pagani, C.D., Ruf, B. (eds) Nonlinear Equations: Methods, Models and Applications. Progress in Nonlinear Differential Equations and Their Applications, vol 54. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8087-9_8
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DOI: https://doi.org/10.1007/978-3-0348-8087-9_8
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