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Zbl 0892.34040
Liu, Zhongdong; Mao, Yiping
Existence theorem for periodic solutions of higher order nonlinear differential equations.
(English)
[J] J. Math. Anal. Appl. 216, No.2, 481-490 (1997). ISSN 0022-247X

The authors prove the existence of a $T$-periodic solution of the equation $$x^{(m)}+ a_{m-1}x^{(m-1)}+ \cdots+ a_1x'+ g(t,x,x',\dots, x^{(m)})= f(t),$$ where $f(t)\equiv f(t+ T)$. Unlike in the majority of similar papers, the nonlinearity $g$ depends explicitly on the highest derivative $x^{(m)}$.
[J.Andres (Olomouc)]
MSC 2000:
*34C25 Periodic solutions of ODE

Keywords: periodic solutions; higher-order equations; nonlinearity depending on the highest-order derivative

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