一类Duffing型方程周期解的存在唯一性和稳定性
Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type
摘要：
考虑一个二阶Duffing型方程。给出了恢复力导数的界，保证了周期解的存在唯一性。此外，唯一的周期解是渐近稳定的急剧指数衰减率。特别地，对于与变量$t$无关的恢复项，得到了保证稳定周期解存在唯一的充要条件.
英文摘要：
We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically stable with sharp rate of exponential decay. In particular, for a restoring term independent of the variable $t$, a necessary and sufficient condition is obtained which guarantees the existence and uniqueness of a periodic solution that is stable.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
