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I wonder where can I find a proof of the following fact: if the mountain pass critical point is non-degenerate, then its Morse index is 1. I am very interested in reading it. In general, I am interested in reading notes on Morse index and MP critical points. So I will be very grateful, if someone can suggest me some notes about that.

Thank in advance.

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Please, check the book of Mawhin and Willem: J. Mawhin, M. Willem, Critical Point Theory and Hamiltonian Systems,Vol. 74 of Applied Mathematical Sciences, Springer–Verlag, 1989 (1989).[

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I think you should have a looks at this paper "Variational and Topological Methods in Partially Ordered Hilbert Spaces" by Helmut Hofer in Mathematische Annalen 1982.

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