Turkish Journal of Mathematics
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, 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