ON THE PERIODIC SOLUTIONS OF COMPLETE SECOND ORDER DIFFERENTIAL EQUATIONS ON HILBERTSPACE

Abstract

For the complete, second order differential equation u (t) = Au (t) + Bu(t) + f(t) (*), 0 ≤ t ≤ T on a Hilbert space E, we find the necessary and sufficient conditions so that (*) has a unique T-periodic solution. Some applications are also given.