Periodic solutions in a given set of differential systems (Q5957164)

Given a nonempty open and bounded subset \(\Theta\subset\mathbb{R}^n\), the authors use a Ważewski-type approach in combination with degree arguments in order to prove a sufficient condition for the existence of solutions, located in \(\Theta\), to the periodic problem NEWLINE\[NEWLINE\dot x= f(t,x),\quad x(0)=x(1),NEWLINE\]NEWLINE where \(f:[0,1]\times\mathbb{R}^n\to\mathbb{R}^n\) satisfies the usual assumptions for the existence of Carathéodory solutions.