## Periodic solutions in a given set of differential systems.(English)Zbl 1001.34035

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 $\dot x= f(t,x),\quad x(0)=x(1),$ where $$f:[0,1]\times\mathbb{R}^n\to\mathbb{R}^n$$ satisfies the usual assumptions for the existence of Carathéodory solutions.

### MSC:

 34C25 Periodic solutions to ordinary differential equations
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### References:

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