Existence of periodic solutions for a nonautonomous differential equation

We consider the nonautonomous differential equation of second order x '' + a(t)x - b(t)x' + c(t)x(2k+1) = 0, where a(t), b(t), c(t) are T-periodic functions and 2 <= l < 2k + 1. This is a generalization of a biomathematical model of an aneurysm in the circle of Willis. We prove the existence of a T-periodic solution for this equation, using a saddle-point theorem.