LAUSR

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