LOCAL INTEGRAL MANIFOLDS FOR NONAUTONOMOUS AND ILL-POSED EQUATIONS WITH SECTORIALLY DICHOTOMOUS OPERATOR

We show the existence and C-k,C-gamma smoothness of local integral manifolds at an equilibrium point for nonautonomous and ill-posed equations with sectorially dichotomous operator, provided that the nonlinearities are C-k,C-gamma smooth with respect to the state variable. C-k,C-gamma local unstable integral manifold follows from C-k,C-gamma local stable integral manifold by reversing time variable directly. As an application, an elliptic PDE in infinite cylindrical domain is discussed.