Electron. J. Diff. Equ., Vol. 2012 (2012), No. 232, pp. 1-8.

Anti-periodic solutions to Rayleigh-type equations with two deviating arguments

Meiqiang Feng, Xuemei Zhang

Abstract:
In this article, the Rayleigh equation with two deviating arguments
$$ x''(t)+f(x'(t))+g_1(t,x(t-\tau_1(t)))+g_2(t,x(t-\tau_2(t)))=e(t) $$
is studied. By using Leray-Schauder fixed point theorem, we obtain the existence of anti-periodic solutions to this equation. The results are illustrated with an example, which can not be handled using previous results.

Submitted September 20, 2012. Published December 21, 2012.
Math Subject Classifications: 34K13, 34K15, 34C25.
Key Words: Rayleigh equation; anti-periodic solution; deviating argument.

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Meiqiang Feng
School of Applied Science
Beijing Information Science and Technology University
Beijing, 100192, China
email: meiqiangfeng@sina.com
Xuemei Zhang
Department of Mathematics and Physics
North China Electric Power University
Beijing, 102206, China
email: zxm74@sina.com

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