Abstract:We discuss the existence of the coupled minimal and maximal quasi-solutions of an initial value problem \ \ u′(t)-h(t)f 1(u)=f 0(t,u) u(0)=u 0\ \ \ \ \ \ \ \ \ where f 0:J×R n→R n satisfies the Carathéodory’s condition,f 1∈C R n,R n ,h∈C J,R ,J= 0,