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

Andres, Jan; Krajc, Bohumil

J. Math. Anal. Appl. 264, No. 2, 495-509 (2001).

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.

Reviewer: Marco Spadini (Firenze)

MSC:

34C25

Periodic solutions to ordinary differential equations

Keywords:

periodic solutions; Brouwer degree; Leray-Schauder degree; Ważewski-type results

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