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

By using topological methods,mainly the degree of a tangent vector field, we establishmultiplicity 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 = R and M = R^2. Doing so, we providemore comprehensive analysis of those cases and find improved conditions.