Existence and uniqueness of periodic solutions
for odd-order ordinary differential equations
Annales Polonici Mathematici, Tome 100 (2011) no. 2, pp. 105-114
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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].
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
Affiliations des auteurs :
Yongxiang Li 1 ; He Yang 1
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author = {Yongxiang Li and He Yang},
title = {Existence and uniqueness of periodic solutions
for odd-order ordinary differential equations},
journal = {Annales Polonici Mathematici},
pages = {105--114},
publisher = {mathdoc},
volume = {100},
number = {2},
year = {2011},
doi = {10.4064/ap100-2-1},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap100-2-1/}
}
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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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