Marino—Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces

2006 ◽  
Vol 186 (1) ◽  
pp. 155-183 ◽  
Author(s):  
Silvia Cingolani ◽  
Giuseppina Vannella
Keyword(s):  
Banach Spaces ◽  
Critical Points ◽  
Morse Indices

ADIABATIC SPECTRAL FLOW AND CHANGE OF MORSE INDICES

1994 ◽  
Vol 09 (15) ◽  
pp. 1369-1375
Author(s):  
HIDEKI ONO ◽  
HIROSHI KURATSUJI
Keyword(s):  
Critical Points ◽  
Morse Index ◽  
Theory Model ◽  
Structure Change ◽  
Spectral Flow ◽  
Action Functional ◽  
One Dimensional ◽  
Physical Systems ◽  
Field Action ◽  
Morse Indices

The concept of the Morse index characterizes the behavior near the critical points of the action functional that governs physical systems. We study the specific feature of Morse indices for the case that there are several number of critical points; on each of these critical points the Morse indices are defined. As a concrete example, we consider a model of one-dimensional field theory model. By using the idea of the adiabatic spectral flow, it is shown that the change of the Morse indices is correlated with the structure change inherent in the solutions of field equation that is controlled by the parameters built in the field action.

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