Existence of periodic solutions for a nonautonomous differential equation

Abstract

We consider the nonautonomous differential equation of second order $x''+ a(t)x-b(t) x^l+c(t)x^{2k+1}=0$, where $a(t),b(t),c(t)$ are $T$-periodic functions and $2\leq l < 2k+1$. 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.