© 2018 Walter de Gruyter GmbH, Berlin/Boston. We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials -(px′)′(t) - r(t)p(t)x′(t) + q(t)x(t) = f(t, x(t)), where the functions p(t) > 0, q(t), r(t) and f(t, x) are C2 and T-periodic in the variable t.
- Periodic orbit
- averaging theory
- quadratic system
- third-order differential equation