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Zbl 1057.34098
Zhang, Zhengqiu; Wang, Zhicheng
Periodic solutions of the third order functional differential equations.
(English)
[J] J. Math. Anal. Appl. 292, No. 1, 115-134 (2004). ISSN 0022-247X

The authors deal with the existence of $2\pi$-periodic solutions of third-order differential equations of the type $$x'''(t)+ a(x'')^{2k-1}(t)+ b(x')^{2k-1}(t)+ cx^{2k-1}(t)+ g(t,x(t-\tau_1), x'(t-\tau_2))= p(t), \tag 1$$ where $p(t+2\pi)= p(t)$, $a$, $b$, $c$, $\tau_1$ and $\tau_2$ are real numbers, $k$ is a positive integer, $g: \bbfR\times \bbfR\times \bbfR\to \bbfR$ is continuous and $2\pi$-periodic with respect to the first variable $t$. The authors derive sufficient conditions for the existence of periodic solutions of (1). To this end, the authors use the continuation theorem from the theory of the coincidence degree, and a priori estimates.
[Messoud A. Efendiev (Berlin)]
MSC 2000:
*34K13 Periodic solutions of functional differential equations

Keywords: Functional-differential equation; Periodic solution; Coincidence degree; Continuation theorem

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