Periodic solutions of a nonlinearn-th order vector differential equation

Summary We investigate a non-autonomous n-th order differential equation for a function x(t) ∈ R^m supposing that the equation contains one nonlinear term only depending on x. Our aim is to prove the existence of at least one periodic solution (with the same period as the external forcing). The conditions developed for the nonlinear term are rather general and do not imply the global boundedness of the solutions. Entrata in Redazione il 21 luglio 1970.