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

Yongxiang Li, and He Yang. "Existence and uniqueness of periodic solutions for odd-order ordinary differential equations." Annales Polonici Mathematici 100.2 (2011): 105-114. <http://eudml.org/doc/280235>.

@article{YongxiangLi2011,
abstract = {The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation $u^\{(2n+1)\} = f(t,u,u^\{\prime \},...,u^\{(2n)\})$, where $f: ℝ × ℝ^\{2n+1\} → ℝ$ is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity $f(t,x₀,x₁,...,x_\{2n\})$ 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].},
author = {Yongxiang Li, He Yang},
journal = {Annales Polonici Mathematici},
keywords = {periodic solutions},
language = {eng},
number = {2},
pages = {105-114},
title = {Existence and uniqueness of periodic solutions for odd-order ordinary differential equations},
url = {http://eudml.org/doc/280235},
volume = {100},
year = {2011},
}

TY - JOUR
AU - Yongxiang Li
AU - He Yang
TI - Existence and uniqueness of periodic solutions for odd-order ordinary differential equations
JO - Annales Polonici Mathematici
PY - 2011
VL - 100
IS - 2
SP - 105
EP - 114
AB - The paper deals with the existence and uniqueness of 2π-periodic solutions for the odd-order ordinary differential equation $u^{(2n+1)} = f(t,u,u^{\prime },...,u^{(2n)})$, where $f: ℝ × ℝ^{2n+1} → ℝ$ is continuous and 2π-periodic with respect to t. Some new conditions on the nonlinearity $f(t,x₀,x₁,...,x_{2n})$ 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].
LA - eng
KW - periodic solutions
UR - http://eudml.org/doc/280235
ER -