Green's function for periodic solutions in alternately advanced and delayed differential systems (Q2025240)

In the paper, the differential system \[ x'(t)=A(t)x(t)+f(t,x(t),x(\gamma(t)))+g(t,x(t),x(\gamma(t))) \] is considered with a piecewise continuous argument deviation \(\gamma\). The existence of an \(\omega\)-periodic solution is studied under the assumption that the corresponding linear system has only the trivial \(\omega\)-periodic solution. By using Krasnoselskii's fixed point theorem, the author proves the existence (resp. the existence and uniqueness) of an \(\omega\)-periodic solution to the given system. Applications and illustrative examples are discussed as well.