Continuation Theorems for Periodic Perturbations of Autonomous Systems

Capietto, A.;Mawhin, Jean;Zanolin, F.
(1992) Transactions of the American mathematical society — Vol. 329, n° 1, p. 41-72 (1992)

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Authors
  • Capietto, A.
    Author
  • Mawhin, JeanUCLouvain
    Author
  • Zanolin, F.
    Author
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' - 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.
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Capietto, A., Mawhin, J., & Zanolin, F. (1992). Continuation Theorems for Periodic Perturbations of Autonomous Systems. Transactions of the American mathematical society, 329(1), 41-72. https://doi.org/10.2307/2154076 (Original work published 1992)