Limit cycles of the sixth-order non-autonomous differential equation

We provide sufficient conditions for the existence of periodic solutions of the sixth-order differential equationx(6)+(1+p2+q2)x....+(p2+q2+p2q2)x¨+p2q2x=εF(t,x,x˙,x¨,x...,x....,x.....),where p and q are rational numbers different from 1, 0, −1 and p ≠ q, ε is small and F is a nonlinear non-autonomous periodic function. Moreover we provide some applications.