Periodic solutions to the Cahn-Hilliard equation with constraint

This paper is concerned with the multidimensional Cahn-Hilliard equation with a constraint. The existence of periodic solutions of the problem is mainly proved under consideration by the viscosity approach. More precisely, with the help of the subdifferential operator theory and Schauder fixed point theorem, the existence of solutions to the approximation of the original problem is shown, and then the solution is obtained by using a passage-to-limit procedure based on a prior estimate.