We prove the existence of a smooth center manifold for several partial differentialequations, including ill posed equations with unbounded nonlinearities. We also provesmooth dependence on parameters with respect to some perturbations, including unboundedones. More concretely, we prove an abstract theorem and present applications to several concrete equations: ill posed Boussinesq, equation and system and nonlinear Laplace equations in cylindrical domains. We also consider the effect of some geometric structures.