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

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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References in corpus (1)

• Harmonic solutions to a class of differential-algebraic equations with separated variables