A KAM theorem of degenerate infinite dimensional Hamiltonian systems (II)

A class of weaker nondegeneracy conditions is given and an existence theorem of invariant tori is prove n for small perturbations of degenerate integrable infinite dimensional Hamiltonian systems under the weaker nondegeneracy conditions. The measure estimates of the parameter set are also given for which invariant tori exist. It is valuable to point out that by the motivation of finite dimensional situation the nondegeneracy conditions may be the weakest. Mainly KAM machine is used to prove the existence of invariant tori. The measure estimates for small divisor conditions, on which the measure estimates of the parameter set are based, will be given in the second paper.