Critical points and infinite-dimensional Hamiltonian systems

We discuss deformation techniques in critical point theory. By introducing on non-metrizable topological spaces Lipschitz partitions of unity we present results on certain existence and uniqueness of solution of ODEs. This allows us to construct deformations on locally convex topological vector spaces. As applications, we develop new methods in critical point theory oriented towards differential equations in infinite-dimensional Hamiltonian mechanics, especially the Schrodinger equation, Dirac equation, diffusion systems, etc.