Branches of Forced Oscillations Induced by a Delayed Periodic Force

Abstract

We study global continuation properties of the set of T-periodic solutions of parameterized second order delay differential equations with constant time lag on smooth manifolds. We apply our results to get multiplicity of T-periodic solutions. Our topological approach is mainly based on the notion of degree of a tangent vector field.

Keywords

• periodic solutions
• forced motion
• delay differential equations
• multiplicity of periodic solutions
• forced motion on manifolds
• degree of a tangent vector field
• 34k13
• 70k40
• 34c25