Periodic solutions for a class of non-autonomous Newton differential equations

Altres ajuts: ICREA AcademiaWe provide sufficient conditions for the existence of periodic solutions of the second-order non-autonomous differential equation x¨=-∇xV(t,x),in R, where V(t,x)=‖x‖22+εW(t,x) with W(t, x) a 2 π-periodic function in the variable t, ε is a small parameter, x∈ R and ∇xV(t,x)=(∂V∂x1,…,∂V∂xn).Note that this is a particular class of non-autonomous Newton differential equations. Moreover we provide some applications