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

作者：Bisconti Luca^*; Spadini Marco

来源：Mathematical Methods in the Applied Sciences, 2015, 38(18): 4760-4773.

DOI：10.1002/mma.3390

• periodic solutions
• ordinary differential equations on manifolds
• multiplicity

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.

• 出版日期2015-12