(ω, Q)-periodic mild solutions for a class of semilinear abstract differential equations and applications to Hopfield-type neural network model

In this paper, we investigate the existence and uniqueness of (omega, Q)-periodic mild solutions for the following problem x ' (t) = Ax(t) + f(t, x(t)), t is an element of R, on a Banach space X. Here, A is a closed linear operator which generates an exponentially stable C0-semigroup and the nonlinearity f satisfies suitable properties. The approaches are based on the well-known Banach contraction principle. In addition, a sufficient criterion is established for the existence and uniqueness of (omega, Q)-periodic mild solutions to the Hopfield-type neural network model.