Rotating periodic integrable solutions for second-order differential systems with nonresonance condition

Authors: YI CHENG, KE JIN, RAVI AGARWAL

Abstract: In this paper, by using Parseval's formula and Schauder's fixed point theorem, we prove the existence and uniqueness of rotating periodic integrable solution of the second-order system $x''+f(t,x)=0$ with $x(t+T)=Qx(t)$ and $\int_{(k-1)T}^{kT}x(s)ds=0$, $k\in Z^+$ for any orthogonal matrix $Q$ when the nonlinearity $f$ satisfies nonresonance condition.

Keywords: Existence, uniqueness, rotating periodic integrable solution, Schauder's fixed point theorem

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