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

摘要

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 = R and M = R-2. Doing so, we provide more comprehensive analysis of those cases and find improved conditions. Copyright (C) 2015 John Wiley & Sons, Ltd.