## Periodic Solutions for a Kind of Third-Order Delay Differential Equations with a Deviating Argument

J. Math. Sci. Univ. Tokyo
Vol. 18 (2011), No. 1, Page 35--49.

Abou-El-Ela, A. M. A.;Sadek, A. I. ;Mahmoud A. M..
Periodic Solutions for a Kind of Third-Order Delay Differential Equations with a Deviating Argument
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Abstract:
In this paper, by using the continuation theorem of coincidence degree theory and analysis techniques, we establish a new result on the existence and uniqueness of a T-periodic solution for the third-order delay differential equation with a deviating argument of the following form $$\dddot{x}(t)+f(t,x(t))\ddot{x}(t)+g(x(t))\dot{x}(t) +h(t,x(t-r(t)))=p(t).$$

Keywords: Continuation theorem, Coincidence degree, Existence and uniqueness, Third-order delay differential equations, Deviating argument.

Mathematics Subject Classification (2010): Primary 34C25.