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July  2019, 18(4): 1695-1709. doi: 10.3934/cpaa.2019080

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

 1 IMAS – CONICET, Universidad de Buenos Aires, Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria - Pabellón I - (C1428EGA), Buenos Aires, Argentina 2 Universidad de Chile, Departamento de Matemáticas, Facultad de Ciencias, Casilla 653, Santiago, Chile

* Corresponding author

Received  May 2018 Revised  August 2018 Published  January 2019

Fund Project: The first author is supported by projects CONICET PIP 11220130100006CO and UBACyT 20020160100002BA.

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.

Citation: Pablo Amster, Mariel Paula Kuna, Gonzalo Robledo. Multiple solutions for periodic perturbations of a delayed autonomous system near an equilibrium. Communications on Pure & Applied Analysis, 2019, 18 (4) : 1695-1709. doi: 10.3934/cpaa.2019080
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