Geodesic
Existence and uniqueness of periodic solutions for odd-order ordinary differential equations
Yongxiang Li1 ; He Yang1
1Department of Mathematics Northwest Normal University Lanzhou 730070, People's Republic of China
Annales Polonici Mathematici, Tome 100 (2011) no. 2, pp. 105-114
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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].
DOI : 10.4064/ap100-2-1
Keywords: paper deals existence uniqueness pi periodic solutions odd order ordinary differential equation u ldots where mathbb times mathbb mathbb continuous pi periodic respect conditions nonlinearity ldots guarantee existence uniqueness presented these conditions extend improve presented cong appl math lett

Yongxiang Li  1   ; He Yang  1

1 Department of Mathematics Northwest Normal University Lanzhou 730070, People's Republic of China 
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Yongxiang Li; He Yang. Existence and uniqueness of periodic solutions
for odd-order ordinary differential equations. Annales Polonici Mathematici, Tome 100 (2011) no. 2, pp. 105-114. doi: 10.4064/ap100-2-1

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