Periodic orbits for perturbed non-autonomous differential equations (Q713129)

The paper deals with non-autonomous differential equations on the cylinder \((t,r)\in \mathcal S^{1}\times \mathbb R^{d}\) which can be written as \[ dr/dt=f(t,r,\varepsilon ). \] Under the assumption that the corresponding unperturbed equation (\(\varepsilon =0\)) has an open continuum of periodic solutions, the authors study the variational equations of low order. The derived results are applied to several families of differential equations with \(d=1,2,3\) including some autonomous polynomial differential equations as well as some non-autonomous Abel differential equations.