We provide sufficient conditions for the existence of periodic solutions of the fourth-order differential equation u''''+ qu''+pu = εF(t,u, u', u'', u'''),where q,p and are real parameters, is small and F is a nonlinear non-autonomous periodic function with respect to t. Moreover we provide some applications. © 2012 Elsevier Inc. All rights reserved.
- Averaging theory
- Fourth-order differential equation
- Periodic orbit