Periodic boundary value problems (PBVP) for integro-differential equations of Volterra type in Banach spaces (Q1180507)

Let \(E\) be a real Banach space, \(I=[0,2\pi]\). The author investigates the periodic boundary-value problem \(u'=f(t,u,Tu)\), \(u(0)=u(2\pi)\), \((Tu)(t)=\int^ t_ 0 S(t,s)u(s)ds\) where \(f\in C[I\times E\times E,E]\), \(S\in C[I\times I,R^ +]\). The results concern the existence of monotone sequences which converge uniformly to the minimal and maximal solutions of this problem.