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Zbl 0748.34025
Capietto, Anna; Mawhin, Jean; Zanolin, Fabio
Continuation theorems for periodic perturbations of autonomous systems. (English)
[J] Trans. Am. Math. Soc. 329, No.1, 41-72 (1992). ISSN 0002-9947; ISSN 1088-6850/e

There is shown the relation between the coincidence degree of the left hand side of an autonomous differential equation $x'-g(x)=0$ in the space of periodic functions with fixed period $\omega$ and the Brouwer degree of $g:\bbfR\sp m\to\bbfR\sp m$. Several continuation theorems for $\omega$-periodic perturbations of autonomous systems are presented. Some extensions to differential equations in flow-invariant ENR's are given.
[P.Drábek (Plzen)]

MSC 2000:: *34C25 Periodic solutions of ODE
47H11 Degree theory

Keywords: coincidence degree; autonomous differential equation; periodic functions; Brouwer degree; continuation theorems; perturbations

Cited in: Zbl 1220.34062 Zbl 0980.47053 Zbl 0961.34034

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