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Transactions of the American Mathematical Society

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Continuation theorems for periodic perturbations of autonomous systems


Authors: Anna Capietto, Jean Mawhin and Fabio Zanolin
Journal: Trans. Amer. Math. Soc. 329 (1992), 41-72
MSC: Primary 34B15; Secondary 34C25, 58F22
DOI: https://doi.org/10.1090/S0002-9947-1992-1042285-7
MathSciNet review: 1042285
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Abstract: It is first shown in this paper that, whenever it exists, the coincidence degree of the left-hand member of an autonomous differential equation

$\displaystyle x' - {\text{g}}(x) = 0$

, in the space of periodic functions with fixed period $ \omega $, can be computed in terms of the Brouwer degree of $ {\text{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.

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DOI: https://doi.org/10.1090/S0002-9947-1992-1042285-7
Article copyright: © Copyright 1992 American Mathematical Society

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