Periodic solutions of systems of nonautonomous ordinary differential equations (Q1106999)

Conditions are established for the existence and uniqueness of a periodic solution of the system of ordinary differential equations \(\dot x_ i=f_ i(t,x_ 1,x_ 2,...,x_ n)\) \((i=1,2,...,n)\), where \(f_ i: {\mathbb{R}}\times {\mathbb{R}}\) \(n\to {\mathbb{R}}\) \((i=1,...,n)\) satisfies Carathéodory conditions in any compactum contained in \({\mathbb{R}}\times {\mathbb{R}}\) nu \(f_ i(t+\omega,x_ 1,x_ 2,...,x_ n)=f_ i(t,x_ 1,x_ 2,...,x_ n),\) R is the set of real numbers. A method of constructing the solution is given.