Continuation theorems for periodic perturbations of autonomous systems
Continuation theorems for periodic perturbations of autonomous systems
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DOI：
10.1090/s0002-9947-1992-1042285-7
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发表时间：
1992
影响因子：
1.3
通讯作者：
A. Capietto;J. Mawhin;F. Zanolin
中科院分区：
文献类型：
--
作者：
A. Capietto;J. Mawhin;F. Zanolin
本文首先证明了，只要存在一个自治微分方程x' - g（x）= 0的左元，它在周期函数空间中的重合度可以用g的Brouwer度来计算。这一结果为自治系统的ω-周期扰动提供了有效的延拓定理。扩展微分方程在流不变ENR的也给出了。
It is first shown in this paper that, whenever it exists, the coincidence degree of the left-hand member of an autonomous differential equation x' - g(x) = 0, in the space of periodic functions with fixed period omega, can be computed in terms of the Brouwer degree of g. This result provides efficient continuation theorems specially for omega-periodic perturbations of autonomous systems. Extensions to differential equations in flow-invariant ENR's are also given.