The optimal gap condition for invariant manifolds
The authors give optimal gap conditions using Lipschitz constants of the nonlinear terms and exponential estimates for the semiflows generated by the linear terms that imply the existence of infinite dimensional Lipschitz invariant manifolds for systems of weakly nonlinear equations on Banach spaces. The results are shown to imply the existence of invariant manifolds for skew-product flows generated by weakly nonlinear nonautonomous equations. Also, generalizations of results for the smoothness of invariant manifolds are given.
scientific article; zbMATH DE number 1492569