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The Morse index theorem for general end conditions. (English) Zbl 1007.58008
The author generalizes Kalish’s formula of the Morse index for the general variational problem with submanifolds as the end conditions. For the Kalish’s formula (in the Riemann case) see Diane Kalish [Trans. Am. Math. Soc. 308, No. 1, 341-348 (1988; Zbl 0652.58016)].
Reviewer’s addition: for the general problems with the stratified terminal submanifolds see S. A. Vakhrameev [J. Math. Sci., New York 71, No. 3, 2434-2485 (1994; Zbl 0835.58006); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat., Novejshie Dostizh. 39, 41-117 (1991; Zbl 0802.58015)].

MSC:
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
58E25 Applications of variational problems to control theory
49N99 Miscellaneous topics in calculus of variations and optimal control
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