# Wydawnictwa / Czasopisma IMPAN / Annales Polonici Mathematici / Wszystkie zeszyty

## Existence and uniqueness of periodic solutions for odd-order ordinary differential equations

### Tom 100 / 2011

Annales Polonici Mathematici 100 (2011), 105-114 MSC: Primary 34C25; Secondary 34B15. DOI: 10.4064/ap100-2-1

#### Streszczenie

The paper deals with the existence and uniqueness of $2\pi$-periodic solutions for the odd-order ordinary differential equation $$u^{(2n+1)}=f(t,u,u',\ldots,u^{(2n)}),$$ where $f: \mathbb R\times\mathbb R^{2n+1}\to\mathbb R$ is continuous and $2\pi$-periodic with respect to $t$. Some new conditions on the nonlinearity $f(t,x_0,x_1,\ldots,x_{2n})$ to guarantee the existence and uniqueness are presented. These conditions extend and improve the ones presented by Cong [Appl. Math. Lett. 17 (2004), 727–732].

#### Autorzy

• Yongxiang LiDepartment of Mathematics
Northwest Normal University
Lanzhou 730070, People's Republic of China
e-mail
• He YangDepartment of Mathematics
Northwest Normal University
Lanzhou 730070, People's Republic of China
e-mail

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