Abstract and Applied Analysis

Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations

Abstract

The existence of multiple periodic solutions of the following differential delay equation ${x}^{\prime}(t)=-f(x(t-r))$ is established by applying variational approaches directly, where $x\in \mathbb{R}$, $f\in C(\mathbb{R},\mathbb{R})$ and $r>0$ is a given constant. This means that we do not need to use Kaplan and Yorke's reduction technique to reduce the existence problem of the above equation to an existence problem for a related coupled system. Such a reduction method introduced first by Kaplan and Yorke in (1974) is often employed in previous papers to study the existence of periodic solutions for the above equation and its similar ones by variational approaches.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 978137, 14 pages.

Dates
First available in Project Euclid: 2 March 2010

https://projecteuclid.org/euclid.aaa/1267538587

Digital Object Identifier
doi:10.1155/2010/978137

Mathematical Reviews number (MathSciNet)
MR2587611

Zentralblatt MATH identifier
1195.34104

Citation

Cheng, Rong; Hu, Jianhua. Variational Approaches for the Existence of Multiple Periodic Solutions of Differential Delay Equations. Abstr. Appl. Anal. 2010 (2010), Article ID 978137, 14 pages. doi:10.1155/2010/978137. https://projecteuclid.org/euclid.aaa/1267538587

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