Periodic solutions of general autonomous system of liénard type

Abstract

This article gives some sufficient conditions for the existence and nonexistence of nonzero periodic solutions of the general autonomous system of Liénard type

The main purpose of this article is to study the problem of how small the extent for the function f ( x, y ) should be to guarantee the existence of nonzero periodic solutions of this system. With some standard additional assumptions, we prove that if

then the system has at least one nonzero periodic solution, otherwise, the system has no nonzero periodic solution.

Keywords:

• Generalized Liénard system
• Periodic solution
• AMS: 34C25

Acknowledgments

The first author expresses his sincere thanks to his supervisor Professor Mats Gyllenberg for careful reading of the manuscript and valuable comments. This work has been supported by the Academy of Finland.

Notes

E-mail: [email protected]

Additional information

Notes on contributors

Jifa Jiang †

E-mail: [email protected]