Massera problem for non-autonomous retarded differential equations (Q1947307)

The existence of an \(\omega\)-periodic mild solution of a reaction-diffusion equation is proven as an application of an abstract result. Starting from an existence result of a fixed point for a multivalued map defined on a nonempty convex set in a Banach space, conditions are established which ensure the existence of an \(\omega\)-periodic mild solution of a nonhomogeneous linear equation. Using the Poincaré map, the authors prove the equivalence between the existence of a bounded mild solution and the existence of an \(\omega\)-periodic mild solution of the considered problem.