Electron. J. Diff. Equ., Vol. 2015 (2015), No. 242, pp. 1-12.

Existence of positive periodic solutions for neutral Lienard differential equations with a singularity

Fanchao Kong, Shiping Lu, Zaitao Liang

Abstract:
By applying Mawhin's continuation theorem, we study the existence of positive periodic solutions for a second-order neutral functional differential equation
$$ ((x(t)-cx(t-\sigma)))''+f(x(t)) x'(t)+g(t,x(t-\delta))=e(t), $$
where g has a strong singularity at x=0 and satisfies a small force condition at $ x=\infty$, which is different from the corresponding ones known in the literature.

Submitted May 6, 2015. Published September 21, 2015.
Math Subject Classifications: 34B16, 34B20, 34B24.
Key Words: Positive periodic solution; neutral differential equation; deviating argument; singular; Mawhin's continuation.

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Fanchao Kong
College of Mathematics and Computer Science
Anhui Normal University
Wuhu 241000, Anhui, China
email: fanchaokong88@yahoo.com
Shiping Lu
College of Mathematics and Statistics
Nanjing University of Information Science and Technology
Nanjing 210044, China
email: lushiping26@sohu.com
Zaitao Liang
Department of Mathematics
College of Science, Hohai University
Nanjing 210098, China
email: liangzaitao@sina.cn

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