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.

DOI

10.3906/mat-2005-63

Keywords

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

First Page

233

Last Page

243

Recommended Citation

CHENG, Y, JIN, K, & AGARWAL, R (2021). Rotating periodic integrable solutions for second-order differential systems with nonresonance condition. Turkish Journal of Mathematics 45 (1): 233-243. https://doi.org/10.3906/mat-2005-63