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Multiple solutions for periodic perturbations of a delayed autonomous system near an equilibrium

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    * Corresponding author 
The first author is supported by projects CONICET PIP 11220130100006CO and UBACyT 20020160100002BA.
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  • Small non-autonomous perturbations around an equilibrium of a nonlinear delayed system are studied. Under appropriate assumptions, it is shown that the number of $ T $-periodic solutions lying inside a bounded domain $ \Omega\subset \mathbb{R}^{N} $ is, generically, at least $ |\chi \pm 1|+1 $, where $ \chi $ denotes the Euler characteristic of $ \Omega $. Moreover, some connections between the associated fixed point operator and the Poincaré operator are explored.

    Mathematics Subject Classification: Primary: 34K13, 47H10; Secondary: 47H11.


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