... These methods allow us to improve the previous results Proofs of the theorems We now give the proof of Theorem 1.1 Proof Let X be the set of vector functions x(t) given by (1.2) and described above ... Tang, Periodic solutions of a class of non-autonomous second-order systems, Journal of Mathematical Analysis and Applications 236 (1999), no 2, 227–235 Martin Schechter: Department of Mathematics, ... is a Hilbert space with norm satisfying n x X = xj j =1 H1 (2.1) Periodic solutions of second-order nonautonomous dynamical systems We also write n x = xj , (2.2) j =1 where · is the L2 (I)...