Twist periodic solutions for differential equations with a combined attractive–repulsive singularity

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Abstract

We study the existence of twist periodic solutions of second order differential equations with an attractive–repulsive singularity. Such twist periodic solutions are stable in the sense of Lyapunov. The proof is based on the third order approximation method in combination with some location information obtained by the averaging method and the method of upper and lower solutions on the reversed order.

Keywords

Twist periodic solutions
Lyapunov stability
Attractive–repulsive singularity
Third order approximation
Averaging method
Upper and lower solutions

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Jifeng Chu was supported by the National Natural Science Foundation of China (Grant No. 11171090) and the Fundamental Research Funds for the Central Universities (Grant No. 2015B19214). Pedro J. Torres was partially supported by project MTM2011-23652, Ministerio de Economía e Innovación, Spain. Feng Wang was supported by the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 15KJB110001).