A remark on the theory of periodic solutions of semilinear differential systems (Q2703934)

Consider the differential system (*) \(dx/dt=A(t,x)x+f(t)\), with \(A\in C(\mathbb{R} \times\mathbb{R}^n, L(\mathbb{R}^n, \mathbb{R}^n))\), \(f\in C(\mathbb{R},\mathbb{R}^n)\). Additionally, \(A\) and \(f\) are \(\omega\)-periodic in \(t\), and \(A\) satisfies a Lipschitz condition with respect to the second variable. Using an equivalent system of integral equations, the author derives conditions guaranteeing the existence of a unique \(\omega\)-periodic solution to (*) as well as two iterative algorithms for its construction.