Duffing方程周期解的精确个数及其稳定性  

Stability and exact multiplicity of periodic solutions of Duffing equations

作　　者：陈红斌[1] 邢慧 殷子健 Chen Hongbin;Xing Hui;Yin Zijian(School of Mathematics and Statistics,Xi'an Jiaotong University,Xi'an 710049,China;Department of Mathematics,Xi'an Polytechnic University,Xi'an 710048,China;College of Science,Northwest A&F University,Xianyang 710048,China)

机构地区：[1]西安交通大学数学与统计学院,陕西西安710049 [2]西安工程大学数学系,陕西西安710048 [3]西北农林科技大学数学系,陕西咸阳712100

出　　处：《纯粹数学与应用数学》2022年第3期358-365,共8页Pure and Applied Mathematics

基　　金：陕西省自然科学基金(2021JQ-662)。

摘　　要：研究了Duffing方程周期解的精确个数及其稳定性.在非线性项具有U-型结构且不假定凸性的条件下,得到了Ambrosetti-Prodi定理.其研究方法主要采用了反极值原理与分歧方法,该方法适用于更为一般的非线性问题.We study the stability and exact multiplicity of periodic solutions of the Duffing equation.We obtain Ambrosetti-Prodi type theorem under U-shaped nonlinearity without convex condition.Our approach based on anti-maximum principle and bifurcation methods can be applied to more general type nonlinearities.

关 键 词：DUFFING方程 周期解 分歧 稳定性 

分 类 号：O178[理学—数学]