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arXiv · 1409.5890

About the notion of non-$T$-resonance and applications to topological multiplicity results for ODEs on differentiable manifolds

Luca Bisconti·Marco Spadini
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Abstract

By using topological methods, mainly the degree of a tangent vector field, we establish multiplicity results for $T$-periodic solutions of parametrized $T$-periodic perturbations of autonomous ODEs on a differentiable manifold $M$. In order to provide insights into the key notion of $T$-resonance, we consider the elementary situations $M = \mathbb{R}$ and $M = \mathbb{R}^2$. So doing, we provide more comprehensive analysis of those cases and find improved conditions.

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Luca Bisconti, Marco Spadini. 2014-09-20. About the notion of non-$T$-resonance and applications to topological multiplicity results for ODEs on differentiable manifolds. https://doi.org/10.1002/mma.3390

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