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

Yongxiang Li; He Yang

Yongxiang Li ; He Yang

Annales Polonici Mathematici, Tome 101 (2011), p. 105-114 / Harvested from The Polish Digital Mathematics Library

Résumé

The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation $u^{(2 n + 1)} = f (t, u, u^{'}, . . ., u^{(2 n)})$ , where $f : ℝ \times ℝ^{2 n + 1} \to ℝ$ is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity $f (t, x ₀, x ₁, . . ., x_{2 n})$ 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].

Publié le : 2011-01-01

Zbl 1222.34046

EUDML-ID : urn:eudml:doc:280235

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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},
     volume = {101},
     year = {2011},
     pages = {105-114},
     zbl = {1222.34046},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-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 101 (2011) pp. 105-114. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap100-2-1/