Constant-sign periodic and almost periodic solutions for a system of integral equations

We consider the following system of integral equationsu(i)(t) = integral(1) g(i)(t, s)f(s, u(1)(s), (...) , u(n)(s))ds, t is an element of I, 1 = i = nwhere I is an interval of R. Our aim is to establish criteria such that the above system has a constant-sign periodic and almost periodic solution ( u(1), u(2) ,..., u(n)) when I is an infinite interval of R, and a constant-sign periodic solution when I is a finite interval of R. The above problem is also extended to that on Ru(i)(t) = integral(R) g(i)(t, s) f(i) (s, u(1) (s), u(2) (s), ... , u(n)(s))ds, t is an element of R, 1 = i = n.