Applications of the Poincare-Birkhoff theorem to impulsive Duffing equations at resonance

作者：Jiang, Fangfang; Shen, Jianhua^*; Zeng, Yanting

来源：Nonlinear Analysis: Real World Applications , 2012, 13(3): 1292-1305.

DOI：10.1016/j.nonrwa.2011.10.006

• Impulsive Duffing equation
• Periodic solution
• Poincare-Birkhoff theorem

Many dynamical systems possess an impulsive dynamical behavior due to abrupt changes at certain instants during the evolution process. The mathematical description of these phenomena leads to impulsive differential equations. In this paper, we present a new approach via the well-known Poincare-Birkhoff theorem to obtain the existence of periodic solutions to impulsive problems. We consider an impulsive Duffing equation, and find the possibility of applying a generalized form of the Poincare-Birkhoff theorem due to Ding to construct infinitely many periodic solutions of the impulsive Duffing equation even in a resonance case.

• 出版日期2012-6
• 单位杭州师范大学