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

Authors

YI CHENG
KE JIN
RAVI AGARWAL

DOI

10.3906/mat-2005-63

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

First Page

233

Last Page

243

Recommended Citation

CHENG, YI; JIN, KE; and AGARWAL, RAVI (2021) "Rotating periodic integrable solutions for second-order differential systems with nonresonance condition," Turkish Journal of Mathematics: Vol. 45: No. 1, Article 14. https://doi.org/10.3906/mat-2005-63
Available at: https://journals.tubitak.gov.tr/math/vol45/iss1/14