Almost periodic solutions of second-order systems with monotone fields on a compact subset

Abstract

We give sufficient conditions for the existence of almost periodic solutions of the second-order differential system: u″= F( t, u), when F∈C 0( R×K, R N) with K is a compact convex subset of R N , and the partial function F( t,.) is monotone for each t∈ R . For existence, we do not assume that F( t,.) is strictly monotone.