Continuation theorems for periodic perturbations of autonomous systems

Capietto, Anna; Mawhin, Jean; Zanolin, Fabio

doi:10.1090/S0002-9947-1992-1042285-7

Continuation theorems for periodic perturbations of autonomous systems
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by Anna Capietto, Jean Mawhin and Fabio Zanolin PDF

Trans. Amer. Math. Soc. 329 (1992), 41-72 Request permission

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 \[ x’ - {\text {g}}(x) = 0\], 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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