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

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.

Show me the PDF file (226 KB), TEX file, and other files for this article.

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

Return to the EJDE web page