Ultimately Periodic Solutions to a Non-Linear Integrodifferential Equation

Let h( ·) be an integrable f u n c t i o n of integral u n i t y , vanishing for negative a r g u m e n t ; let a, to, a n d # ( 0 ) be c o n s t a n t s ; a n d let / ( · ) be a periodic f u n c t i o n of period ( s a y ) 2ir. It is of interest to know w h a t choices of /*(·)> a , .r(0), and / ( · ) give rise to asymptotically periodic solutions of t h e e q u a t i o n x = a> -- a f hit u ) f ( x ( u ) ) d u (t £ 0 ) .