About the notion of non-\(T\)-resonance and applications to topological multiplicity results for ODEs on differentiable manifolds (Q2795246)

The authors study the periodic problem related to a differential equation of the type NEWLINE\[NEWLINE \dot x=g(x)+\lambda f(t,x). NEWLINE\]NEWLINE Here, \(g:M\to{\mathbb R}^k\) and \(f:{\mathbb R}\times M\to{\mathbb R}^k\) are continuous tangent vector fields on a boundaryless manifold \(M\), and \(f\) is \(T\)-periodic in its first variable, while \(\lambda\) is a nonnegative small real parameter. They prove a multiplicity result of \(T\)-periodic solutions under some conditions related to the degree of tangent vector fields. Some illustrative examples are considered, together with several computer generated bifurcation diagrams.