Infinite Dimensional Morse Theory and Multiple Solution Problems

According AP(M assume assumption Banach manifold Banach space boundary bounded Chapter choose cohomology compact condition convex Corollary critical groups critical manifold critical orbits critical point theory critical set critical value deformation retract deformation theorem denote df(x eigenvalues equation exists f satisfies fc-e finite dimensional Finsler Finsler manifold Fixg Floquet multiplier function f G-invariant Hamiltonian systems harmonic maps Hilbert space homeomorphism homotopy implies isolated critical point isomorphism Lemma let f Morse index Morse inequalities Morse lemma Morse theory neighborhood nondegenerate nontrivial solutions obtain operator pair problem prove respect Riemannian Section sequence singular homology strong deformation retract subset subspace Suppose that f Theorem 5.2 topological vector field verify φο