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arXiv · 1804.05616

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

Pablo Amster·Mariel P. Kuna·Gonzalo Robledo
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Abstract

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 $\Omega\subset \R^N$ 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 Poincar\'e operator are explored.

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Pablo Amster, Mariel P. Kuna, Gonzalo Robledo. 2018-04-16. Multiple solutions for periodic perturbations of a delayed autonomous system near an equilibrium. https://arxiv.org/abs/1804.05616

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