Morse Theory on Banach Manifolds

Let M be a C~2- Finsler manifold modeled on a Banach space, and let f be a C~2-real-valuedfunction defined on M. Using the A-gradient vector field which was introduced in [31] we give a suitable def-inition for nondegenegacy of critical points of f, then generalize the Morse handle-body decomposition theorem and the Morse inequalities to a kind of Banach manifolds. A generalization in the reflexive case hasbeen done in [31] .