Electron. J. Diff. Equ., Vol. 2015 (2015), No. 151, pp. 1-12.

Periodic solutions for Lienard differential equations with singularities

Shengjun Li, Fang-fang Liao, Wenya Xing

Abstract:
In this article, we study the second-order forced Lienard equation x''+f(x)x'+g(x)=e(t). By using the topological degree theory, we prove that the equation has at least one positive periodic solution when g admits a repulsive singularity near the origin and satisfies some semilinear growth conditions near infinity. Recent results in the literature are generalized and complemented.

Submitted November 2, 2014. Published June 10, 2015.
Math Subject Classifications: 34C25.
Key Words: Periodic solution; singular systems; topological degree.

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Shengjun Li
College of Information Sciences and Technology
Hainan University
Haikou 570228, China
email: shjli626@126.com
Fang-fang Liao
Nanjing College of Information Technology
Nanjing 210046, China
email: liaofangfang8178@sina.com
Wenya Xing
College of Information Sciences and Technology
Hainan University
Haikou 570228, China
email: wenyaxing@hainu.edu.cn

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