Morse Index Computations for a Class of Functionals Defined in Banach Spaces
Silvia Cingolani, Giuseppina Vannella · Birkhäuser Basel eBooks · 2003
In Morse theory the behavior of a C 2 Euler functional F , defined on a Hilbert space H ,near its critical points can be described by the estimates of the critical groups in 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 of F , at level c = F(u). We call the qth critical group of F at u, q = 0, 1, 2,…, where Hq (A , B) stands for the qth Alexander-Spanier cohomology group of the pair (A, B) with coefficients in 1K (cf. [2]). These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.