Attractor of the generalized Cahn–Hilliard equation, on which all solutions are unstable

We consider the generalized Сahn–Hilliard equation supplemented by periodic boundary conditions. For the considered boundary-value problem, we obtain sufficient conditions for the existence of a two-dimensional local attractor formed by time-periodic solutions that are unstable in the sense of A. M. Lyapunov. The study is based on asymptotic methods and some methods of the theory of infinite-dimensional dynamical systems, such as the method of integral manifolds and the theory of normal forms.